LESSON #4 - INVERSES OF FUNCTIONS AND FUNCTION NOTATION PART COMMON CORE ALGEBRA II You will recall from unit 1 that in order to find the inverse of a function, ou must switch and and solve for. Also, for a function, f(), the inverse function is written as Eercise #: Find (a) f () = -3 + f 1 ( ). (b) f 1 ( ). 1 f ( ) 5 1 The inverses of polnomial and rational functions can also be found. Eercise #3: Find formulas for the inverse of each of the following simple rational or polnomial functions. 3 (a) g ( ) (b) h ( ) (c) 3 ( ) (d) f( ) 3 4 4 (e) 4 (f) f 5 ( ) ( 4) 6 Modified from emathinstruction, RED HOOK, NY 1571, 015
In the net lesson, we will be working on transforming functions. For this lesson, we will practice writing new functions that are related to these transformations. Eercise #4: The following table includes two parent functions and a quadratic function. Complete each of the following function changes. You do not need to simplif the resulting function. Do not do the last column. Each function change is written as if the function were g(). Make the same change to m() and h(). Function Change f(-) A. Cubic Parent Function g( ) 3 B. Square Root Parent Function m( ) C. Quadratic Function h ( ) 4 3 Transformation -f() f(+) f()- f(-)+5 3f() f() ***** 1 ( ) f 1 f 3 f( 3) f( ) 5 ***** ***** ***** Modified from emathinstruction, RED HOOK, NY 1571, 015
3 LESSON #4 - INVERSES OF FUNCTIONS AND FUNCTION NOTATION PART COMMON CORE ALGEBRA II HOMEWORK 1. Find formulas for the inverse of each of the following functions. (a) 5 (b) 3 4 (c) f () = - 3 + 3 (d) g() = -( +1) 3 + (e) h() = 3-3 (f) g() = 1-1 (g) 5 ( 4) 5 (h) 4 3 Modified from emathinstruction, RED HOOK, NY 1571, 015
. Complete the following table. Column A and B are parent functions, and Column C is a cubic function. NOTE: Each function change is written as if the function were f(). Make the change same change to j() and g(). You do not need to simplif. 4 Function Change A. Absolute Value Parent Function f ( ) B. Quartic Parent Function j( ) 4 C. Cubic Function g 3 ( ) 4 3 6 f(-) -f() f(-4) f()+1 f(+3)- f() f(3) 1 ( ) 3 f f 1 4 f( 1) f( ) 6 Modified from emathinstruction, RED HOOK, NY 1571, 015
5 LESSON #43 FUNCTION TRANSFORMATIONS COMMON CORE ALGEBRA II In the previous lesson, we worked with function changes such as f(-) and f(+3). Each of these changes causes a predictable change in the graph of the function known as a transformation. For eample, making the negative, f(-), will alwas cause the graph to change in the same wa. The easiest function to see all of the transformations is the square root parent function. Eercise #1: Go back to lesson #7, graph the square root parent function as Y1 and each of the changes (transformations) as Y. Determine the transformation that occurred for each problem, and write it in the last column. Eercise #: Summarize our findings in the table below. Function Notation Transformation Groups of Transformations f(-) -f() f(+a) f(-a) f()+a f()-a af() where a 1 af() where 0 a 1 f(a) where a 1 f(a) where 0 a 1 Note: We will be working with horizontal stretches and compressions more etensivel in the net unit. Modified from emathinstruction, RED HOOK, NY 1571, 015
6 Eercise #3: What is the equation of the absolute value parent function, a()=, after each of the following transformations. a. Shift Right 3 b. Reflection in the -ais. c. Shift Down d. Vertical Stretch of 3. e. Reflection in the -ais f. Shift left 3, up 4. g. Vertical Compression of 1. Eercise #4: The function f function, g, is defined b g f is shown on the grid below. A second 3 1. (a) Identif how the graph of f has been transformed to produce the graph of g and sketch it on the grid. (b) A third function, h, is defined b h()= f (). Identif how the graph of f has been transformed to produce the graph of h and sketch it on the grid. (Note: The maimum of h will be off the grid). Eercise #5: If the parabola = were shifted 6 units left and units down, its resulting equation would be which of the following? Verif b graphing our answer and seeing if its turning point is at (-6,-). (1) = ( + 6) + (3) = ( - 6) - () = ( + 6) - (4) = ( - 6) + Modified from emathinstruction, RED HOOK, NY 1571, 015
7 Eercise #6: The graph of a function (b) the graph of f. f is shown below on two grids. Sketch (a) the graph of f and (a) Graph and label. (b) Graph and label Eercise #7: Determine an equation for the linear function g 5 7 -ais. Label our equations. both after a reflection in the -ais and Eercise #8: If the point 3,1 lies on the graph of the function f, which of the following points must lie on the graph of 3 f? (1) 9, 36 (3) 3, 4 () 3, 36 (4) 9,1 Eercise #9: If f 5 3 and is which of the following? g is the reflection of f across the -ais, then an equation of g (1) g 5 3 (3) g 5 3 () g 5 3 (4) g 5 3 Modified from emathinstruction, RED HOOK, NY 1571, 015
8 LESSON #43 - FUNCTION TRANSFORMATIONS COMMON CORE ALGEBRA II HOMEWORK 1. What is the equation of the quintic parent function, f ()= 5, after each of the following transformations? You do not need to simplif. a. Shift left 4 b. Reflection in the -ais c. Shift Up 1 d. Vertical Compression of 1 4 e. Reflection in the -ais f. Shift right 5, down g. Vertical Stretch of 3. Which of the following represents the turning point of f ()=( -8) -4? (1) (-8,-4) (3) (-8,4) () (8,4) (4) (8,-4) 3. Consider the quadratic function f ()= -4-5. The quadratic functions g and h are defined b the formula, g()= f () and h()= 1 f (). Determine formulas for both g and h in standard form. 4. Which of the following equations would represent the graph of the parabola reflection in the -ais? 3 4 1 after a (1) () 3 4 1 (3) 3 4 1 (4) 3 4 1 3 4 1 Modified from emathinstruction, RED HOOK, NY 1571, 015
5. If the point 3, 5 lies on the graph of a function h then which of the following points must lie on the graph of the function h? (1) 3, 5 (3) 5, 3 () 3, 5 (4) 3, 5 6. If the point 6,10 lies on the graph of f graph of 1 f? (1) 3, 5 (3) 6, 5 () 3,10 (4) 1, 0 7. If the quadratic function f has a turning point at 3, 7 defined b g f (1) 7,1 (3) 4, 5 () 1,1 (4) 4, 5 8. The graph of 4 5 have a turning point? then which of the following points must lie on the then where does the quadratic function g f 4 is show below on two separate grids. Give an equation and sketch a graph for the functions (a) f and (b) f. 9 (a) (b) Modified from emathinstruction, RED HOOK, NY 1571, 015
10 9. Given the function f shown graphed on the grid, create a graph for each of the following functions and label on the grid. (a) g f (b) h f 3 (c) k ( ) = 1 f () 10. The graph of the function f is shown on the grid below. The function g is defined b the formula f g 3 1. (a) Graph and label g on the aes. (b) What is the smallest solution to the equation f g? (c) If h g 3, eplain wh the equation h f has no solutions. Modified from emathinstruction, RED HOOK, NY 1571, 015
11 LESSON #44 MULTIPLE TRANSFORMATIONS COMMON CORE ALGEBRA II The following activit will help ou start to think about multiple transformations. Eercise #1: Identif the parent function for each transformation. Draw arrows to each transformation that has happened to the parent function and identif them. a. g( ) 3 7 b. 3 7 c. h( ) d. r()=5( -3) -9 Eercise #: Consider the function, g()= - +5 +3 (a) Graph the function =g() on the grid shown. (b) Describe the transformations that have occurred to the graph of = to produce the graph of =g(). Specif the transformations and the order. Eercise #3: How would the graph of the function h() compare to the graph of f() if h is defined b the formula h()= - f (-)? Modified from emathinstruction, RED HOOK, NY 1571, 015
1 Eercise #4: Which of the following equations represents the graph shown below? (1) 3 4 (3) 3 4 () 3 4 (4) 3 4 g Eercise #5: Consider the function 4. What two transformations have occurred to the graph of to produce the graph of g? Specif the transformations and the order in which the occurred. Note that there eists more than one correct answer. Graph on our calculator to verif. Eercise #6: If the quadratic function function h g 3 5? (1) It has a -intercept of -5. () It has a -intercept of 1. (3) It has a -intercept of -15. (4) It has a -intercept of 31. g has a -intercept of 1, which of the following is true about the Eercise #7: The graph of 1 3. h is shown below. The function f is defined b f h (a) What three transformations have occurred to the graph of h to produce the graph of f? Specif the transformations and the order the occurred in. (b) Graph and label the function that contains h. f on the grid below Modified from emathinstruction, RED HOOK, NY 1571, 015
Eercise #8: The function 3 f h h has a range given b the interval,10. The function f 8. Which of the following gives the range of (1) 11, 3 (3) 15, 7 () 8,1 (4) 6, 3 f? 13 is defined b Modified from emathinstruction, RED HOOK, NY 1571, 015
14 LESSON #44 - MULTIPLE TRANSFORMATIONS COMMON CORE ALGEBRA II HOMEWORK 1. For each of the following functions, identif the parent function. In the last column, identif the transformations that occurred on the parent function and their order. Modified from emathinstruction, RED HOOK, NY 1571, 015
. If the function h is defined as vertical stretch b a factor of followed b a reflection in the -ais of the function f then h 1 f (1) f (3) 1 () f (4) f 15 3. If the graph of is compressed b a factor of 1 3 in the -direction and then shifted 4 units down, the resulting graph would have an equation of (1) 1 3 4 (3) 4 3 () 3 4 (4) 1 3 4 4. The quadratic function f has a turning point at 3,6. The quadratic f turning point of (1), 9 (3) 3, 7 () 1, 7 (4) 1, 9 3 3 would have a 5. The graph of f is shown below. Consider the function g defined b g f 3. (a) What two transformations have occurred to the graph of f in order to produce the graph of g? Specif both the transformations and their order. (b) Graph and label g Modified from emathinstruction, RED HOOK, NY 1571, 015
16 LESSON #45 - EVEN AND ODD FUNCTIONS COMMON CORE ALGEBRA II Recall that functions are simpl rules that convert inputs into outputs. These rules then get placed into various categories, such as linear functions, eponential functions, quadratic functions, etcetera, based on shared characteristics. In this lesson ou will learn another wa to classif some functions that have useful smmetries. EVEN AND ODD FUNCTIONS A function is known as even if for ever value of in the domain of. A function is known as odd if ever value of in the domain of. The terms even function and odd function come from the properties of power functions that have an even eponent or an odd eponent, respectivel. Eercise #1: Draw the following sketches. Identif the tpe of smmetr for the graph and eplain how this makes sense based on the definition above. (a) Draw a basic sketch of an even power function in the form, where a and b are positive. (b) Draw a basic sketch of an odd power function in the form, where a and b are positive. Modified from emathinstruction, RED HOOK, NY 1571, 015
Eercise #3: Consider the partial graph of the function f function if in (a) (a) even f is even and in (b) f 17 shown twice below. Sketch the other half of the is odd. The three coordinate pairs are listed to help ou plot. (b) odd 0, 0, 3, 5, 7, 0, 0, 3, 5, 7, Eercise #4: g 4. Eercise #5: Let's investigate 3 (a) Use our calculator's table option to fill in the following table. What tpe of function is this? Eplain. 3 1 0 1 3 g (b) Sketch a graph of the window indicated. g using our calculator and Modified from emathinstruction, RED HOOK, NY 1571, 015
Determine if the functions on the left side are Even, Odd, or neither. Place a check in the appropriate column. At the bottom of the sheet, use the total number of checks in each column to see if the stated equation is true. Check our work if the epression does not equal. Use a table, graph, or algebraic work. 18 COMPLETE THIS PAGE AS A PART OF YOUR HOMEWORK. Modified from emathinstruction, RED HOOK, NY 1571, 015
19 FLUENCY LESSON #45 - EVEN AND ODD FUNCTIONS COMMON CORE ALGEBRA II HOMEWORK 1. Complete the previous page.. Given the partiall filled out table below for f, fill out the rest of it based on the function tpe. (a) Even (b) Odd 3 1 0 1 3 5 7 4 4 3 1 0 1 3 5 7 0 4 3. Half of the graph of f is shown below. Sketch the other half based on the function tpe. (a) Even (b) Odd Modified from emathinstruction, RED HOOK, NY 1571, 015
0 5. If f is an even function and f 3 5 then what is the value of 4 f 3 f 3? (1) 30 (3) 10 () 60 (4) 6 6. Which of the following functions is even? Show algebraicall how ou arrived at our choice. (1) 4 (3) 9 () 6 (4) 4 7. The function f 4 is either even or odd. Determine which b eploring the function using tables on our calculator. Cop the table. Show algebraicall that the choice is correct. REASONING 8. Even functions have smmetr across the -ais. Odd functions have smmetr across the origin. Can a function have smmetr across the -ais? Wh or wh not? Modified from emathinstruction, RED HOOK, NY 1571, 015
1 LESSON #46 - CIRCLES AND SYSTEMS COMMON CORE ALGEBRA II We will start this lesson b reviewing part of what ou learned about circles in common core geometr. THE EQUATION OF A CIRCLE A circle whose center is at and whose radius is r is given b: Eercise #1: Which of the following equations would have a center of 3, 6 and a radius of 3? (1) 3 6 9 (3) 3 6 3 () 3 6 9 (4) 3 6 3 Eercise #: For each of the following equations of circles, determine both the circle s center and its radius. If its radius is not an integer, epress it in simplest radical form and rounded to the nearest tenth. (a) 7 100 (b) 5 8 4 (c) 11 (d) 1 1 (e) 3 49 (f) 6 5 18 (g) 64 (h) 4 0 (i) 57 Eercise #3: Based on our answers, graph circles d, g, and h on the grid below. Label each circle. Modified from emathinstruction, RED HOOK, NY 1571, 015
In Unit # ou learned how to solve sstems of equations involving a quadratic equation and a linear equation. Now we will work with sstems that involve a linear equation and a circle. These can be solved both algebraicall and graphicall. 1 Eercise #4: Solve the following sstem of equations both algebraicall and graphicall. 5 Algebraicall: Graphicall: 7 Eercise #5: Solve the following sstem of equations both algebraicall and graphicall: ( ) ( ) 9 Algebraicall: Graphicall: Modified from emathinstruction, RED HOOK, NY 1571, 015
3 5 Eercise #6: Solve the following sstem of equations both algebraicall and graphicall: 97 Algebraicall: Graphicall: Note: It can be difficult to find the eact points of intersection if the circle is not graphed perfectl. An algebraic method is recommended. Modified from emathinstruction, RED HOOK, NY 1571, 015
4 FLUENCY LESSON #46 - CIRCLES AND SYSTEMS COMMON CORE ALGEBRA II HOMEWORK 1. Each of the following is an equation of a circle. State the circle s center and radius. If its radius is not an integer, epress it in simplest radical form and rounded to the nearest tenth. (a) 50 (b) 3 7 36 (c) 5 1 64 (d) 6 6 0 (e) 1 (f) 3 00. Which of the following is true about a circle whose equation is (1) It has a center of 5, 3 and an area of 1. () It has a center of 5, 3 and a diameter of 6. (3) It has a center of 5, 3 and an area of 36. (4) It has a center of 5, 3 and a circumference of 1. 5 3 36? 3. Which of the following represents the equation of the circle shown graphed below? (1) 3 16 () 3 4 (3) 3 4 (4) 3 16 Modified from emathinstruction, RED HOOK, NY 1571, 015
5 10 7. Solve the following sstem of equations both algebraicall and graphicall. 58 Algebraicall: Graphicall: 8. Find the intersection of the circle ( 3) ( 4) 9 and 4 both algebraicall and graphicall. Algebraicall: Graphicall: Modified from emathinstruction, RED HOOK, NY 1571, 015
6 LESSON #47 - SYSTEMS OF LINEAR EQUATIONS COMMON CORE ALGEBRA II Eercise #1: Solve each of the sstems of equations b elimination. (a) 3 9 (b) 4 3 5 3 8 10 7 You should be ver familiar with solving two-b-two sstems of linear equations (two equations and two unknowns). These linear sstems serve as the basis for a field of math known as Linear Algebra. Eercise #: Consider the three-b-three sstem of linear equations shown below. Each equation is numbered in this first eercise to help keep track of our manipulations. (1) () (3) z 15 6 3 z 35 4 4 z 14 (a) The addition propert of equalit allows us to add two equations together to produce a third valid equation. Create a sstem b adding equations (1) and () and (1) and (3). Wh is this an effective strateg in this case? (b) Use this new two-b-two sstem to solve the three-b-three. Modified from emathinstruction, RED HOOK, NY 1571, 015
Just as with two b two sstems, sometimes three-b-three sstems need to be manipulated b the multiplication propert of equalit before we can eliminate an variables. Eercise #3: Consider the sstem of equations shown below. Answer the following questions based on the sstem. 4 3z 6 4 z 38 (b) Solve the two-b-two sstem from (a) and find the final solution to the three-b-three sstem. 5 7z 19 (a) Which variable will be easiest to eliminate? Wh? Use the multiplicative propert of equalit and elimination to reduce this sstem to a two-b-two sstem. 7 Modified from emathinstruction, RED HOOK, NY 1571, 015
You can easil check our solution to an sstem of equations b storing our answers for each of the variables and making sure the make each of the equations true. This is especiall useful if ou get a multiple choice question on this topic. Use the storing method to solve the problem below. 8 Eercise #4: Which ordered triple represents the solution to the sstem of equations? 3z 11 4z 3 5 z 18 a. (-1,1,-4) b. (1,3,-) c. (3,8,1) d.(,-3,0) Eercise #5: Solve the sstem of equations shown below. Show each step in our solution process. 4 3z 3 5 3z 37 4z 7 These are challenging problems onl because the are long. Be careful and ou will be able to solve each one of these more comple sstems. Modified from emathinstruction, RED HOOK, NY 1571, 015
9 LESSON #47 - SYSTEMS OF LINEAR EQUATIONS COMMON CORE ALGEBRA II HOMEWORK FLUENCY 1. Solve the following sstems of equations algebraicall. (a) 4 8 3 3 (b) 3 4 4. Show that 10, 4, and z 7 is a solution to the sstem below without solving the sstem formall. z 5 4 5z 1 8z 3 3. Solve the following sstem of equations. Carefull show how ou arrived at our answers. 4 z 1 z 13 3 5z 70 Modified from emathinstruction, RED HOOK, NY 1571, 015
4. Algebraicall solve the following sstem of equations. There are two variables that can be readil eliminated, but our answers will be the same no matter which ou eliminate first. 5 z 35 3 4z 31 3 z 3 30 5. Algebraicall solve the following sstem of equations. This sstem will take more manipulation because there are no variables with coefficients equal to 1. 3 z 33 4 5 3z 54 6 8z 50 Modified from emathinstruction, RED HOOK, NY 1571, 015
31 LESSON #48 FOCUS AND DIRECTRIX OF A PARABOLA PART 1 COMMON CORE ALGEBRA II Materials: 1 sheet patt paper, 1 pencil, 4 colored pencils, ruler 1. Use ruler to draw a straight line with one to two ruler-widths from the bottom of the patt paper. Fold paper in half, folding line upon itself making a crease, mark a point above the line on this crease 3. Make several creases in which the line coincides with the point 4. Using a one of the colored pencils outline the shape that the creases form 5. Draw a sketch of the line, the point, and the shape formed in the tetbo below. DEFINITION OF A PARABOLA A parabola is a special curve shaped like an arch. An point on a parabola is at an equal distance from.. * a fied straight line,, and *a fied point, the Label each of the above in the tetbo with a second color. The ais of smmetr is the line that divides a parabola into two parts that are mirror images. The verte of a parabola is the point at which the parabola intersects the ais of smmetr. On the coordinate plane, the coordinates of the verte are represented b the general point (h,k). The verte is also the directl between the focus and directri. Draw the ais of smmetr and the verte in the tetbo above with a third color and label them. The directed distance from the verte to the focus is represented b the variable, p. This new variable p is one ou'll need to be able to work with when writing equations of parabolas. Label p in the tetbo with the fourth color. Modified from emathinstruction, RED HOOK, NY 1571, 015
3 GEOMETRIC DEFINITION OF A PARABOLA A parabola is the set of all points (,) in a plane that are equidistant from a fied line (directri) and a fied point (focus) not on the line. The standard form of the equation of a parabola with a vertical ais of smmetr when the verte (h,k) and the p value are known is If the lead coefficient is positive: the parabola opens up. If the lead coefficient is negative: the parabola opens down. 1 ( ) h k 4 p When the ais of smmetr is a horizontal ais, the formula is: 1 ( ) k h 4 p If the lead coefficient is positive: the parabola opens right. If the lead coefficient is negative: the parabola will open left. The important difference in the two equations is which variable is squared: for regular (vertical) parabolas, is squared; for sidewas (horizontal) parabolas, is squared. Note: the values of h and k are switched as well so that the -value of the verte is with the -variable. For the first da, we will be focusing on parabolas with vertical directries Eercise #1: For each of the following equations of a parabola (a) state whether it opens up or down and identif the (b) verte, (c) p-value, (d) focus, and (e) the equation of the directri. 1. 1 ( 3) 4 1 (a) Opens up or down (b) Verte (c) p-value (d) Focus (e) Equation of directri Modified from emathinstruction, RED HOOK, NY 1571, 015
33 1. 6 4 (a) Opens up or down (b) Verte (c) p-value (d) Focus (e) Equation of directri 3. 8( 8) ( 7) (a) Opens up or down (b) Verte (c) p-value (d) Focus (e) Equation of directri Modified from emathinstruction, RED HOOK, NY 1571, 015
34 4. ( 3) (a) Opens up or down (b) Verte (c) p-value (d) Focus (e) Equation of directri Eercise #: Write the equation of a parabola with each of the following qualities. It ma be helpful to draw a sketch of the parabola first. a) Write the equation of a parabola whose verte is (,0) and directri is = 6. b) Write the equation of a parabola whose directri is = and focus is (-1,8). Modified from emathinstruction, RED HOOK, NY 1571, 015
35 LESSON #48 FOCUS AND DIRECTRIX OF A PARABOLA PART 1 COMMON CORE ALGEBRA II HOMEWORK For each of the following equations of a parabola (a) state whether it opens up or down and identif the (b) verte, (c) p-value, (d) focus, and (e) the equation of the directri. 1. 1 ( 3) 1 8 (a) Opens up or down (b) Verte (c) p-value (d) Focus (e) Equation of directri 1. 4 ( 4) 0 (a) Opens up or down (b) Verte (c) p-value (d) Focus (e) Equation of directri 3. 1( 6) ( 4) (a) Opens up or down (b) Verte (c) p-value (d) Focus (e) Equation of directri Modified from emathinstruction, RED HOOK, NY 1571, 015
36 4. ( 1) 4 (a) Opens up or down (b) Verte (c) p-value (d) Focus (e) Equation of directri For the following problems, it ma be helpful to sketch the parabola on graph paper. 5. Write the equation of a vertical parabola whose verte is (-1,4) and p-value is 3. 6. Write the equation of a parabola whose verte is (3,9) and focus is (3,6). 7. Write the equation of a parabola whose verte is (0,1) and directri is = -. 8. Write the equation of a parabola whose directri is = -1 and focus is (,-5). Modified from emathinstruction, RED HOOK, NY 1571, 015
37 LESSON #49 FOCUS AND DIRECTRIX OF A PARABOLA PART COMMON CORE ALGEBRA II Eercise #1: Write the general equation of a parabola that has a vertical ais of smmetr. Eercise #: Write the general equation of a parabola that has a horizontal ais of smmetr. Eercise #3: For each of the following equations of a parabola (a) state whether it opens right, left, up, or down and identif the (b) verte, (c) p-value, (d) focus, and (e) the equation of the directri. 1. 1 ( ) 3 4 (a) Opens (b) Verte (c) p-value (d) Focus (e) Equation of directri. 1 5 ( 3) 16 (a) Opens (b) Verte (c) p-value (d) Focus (e) Equation of directri Modified from emathinstruction, RED HOOK, NY 1571, 015
38 3. 4( 6) (a) Opens (b) Verte (c) p-value (d) Focus (e) Equation of directri 4. ( 1) 8 4 (a) Opens (b) Verte (c) p-value (d) Focus (e) Equation of directri 5. Write an equation for the set of points which are equidistant from the origin and the line = -. 6. Write the equation of a parabola whose focus is (3,1) and directri is = 5. 7. Write an equation for the set of points which are equidistant from (4,-) and the line = 4. Modified from emathinstruction, RED HOOK, NY 1571, 015
LESSON #49 FOCUS AND DIRECTRIX OF A PARABOLA PART COMMON CORE ALGEBRA II HOMEWORK For each of the following equations of a parabola (a) state whether it opens right, left, up, or down and identif the (b) verte, (c) p-value, (d) focus, and (e) the equation of the directri. 39 8. 1 ( 3) 1 (a) Opens (b) Verte (c) p-value (d) Focus (e) Equation of directri 9. 1 1 ( 3) 0 (a) Opens (b) Verte (c) p-value (d) Focus (e) Equation of directri 10. ( 1) 1 (a) Opens (b) Verte (c) p-value (d) Focus (e) Equation of directri Modified from emathinstruction, RED HOOK, NY 1571, 015
40 11. ( 3) 8( 5) (a) Opens (b) Verte (c) p-value (d) Focus (e) Equation of directri 1. Write the equation of the parabola with focus (1,6) and directri = 10. 13. Write an equation for the set of points which are equidistant from (0,) and the -ais. 14. Write the equation of the parabola with focus (-,0) and directri the -ais. 15. Write the equation for the set of points equidistant from (,3) and = -3 Modified from emathinstruction, RED HOOK, NY 1571, 015