ALGEBRA 1 Ch 8 Closure - Quadratic Functions Name: il-1-9cabulary: )ial -gr-aphial5lfarxg -vertexeisrnialeting-the,square- -solutions- -steis4u-nstio -elifference-of-se -standar-el-form- -factor- seffeet-setuare4rinanaial- -411144 -y-intereept- -fetetereel-ccrrnptetety -week:tot- -zeros- -factored-fami-. 4tuadratie-equation- `---tero-prot hlet-.4afes9eity..4ereriefeetang4e This organizes x and y values into columns and rows. 2. The story part of a problem is called this. 3. This is what the answer is called when adding. oof 4. This is what the answer is called when multiplying. Al.,r) (M. nel 5. This is a function that when graphed has horizontal segments that are not continuous. 61 614 IN* r(.1-..? 6. A polynomial with only one term. Y1.5' ft (a (. 7. A polynomial that has only two terms. eel 'ell 8. An equation with a highest exponent of 2. )ti bo I 9. When a quadratic equation is graphed, it creates this. m yvel-r. fry- 10. A parabola has this characteristic since a point on one side of a vertical line that goes through the vertex can be reflected to the other side of the line..,,, m, 4.-ereiivet- 11. This is where a graph crosses the x-axis. EX: (x,0). 0 'ret 12. This is where a graph crosses the y-axis. EX: (0, y). 13. This is the lowest point or highest point on a parabola. It is located on the line of symmetry. 14. A quadratic expression written like: 15. A quadratic expression written like: y = x2 x- 2 y = (x +1)(x -2) 16. A quadratic expression written like: y=(x+0 2-2 AxA: ver#e_y 17. The values for x that make an equation true. This is another name for the solution of a quadratic expression. It is usually found by using square roots.
Zeros 19. This is another name for solutions, roots, or x-intercepts. To find these, set an equation equal to zero and solve for x. vree,/-4., e, 20. A diagram that helps you to multiply polynomials. -reke-1-4 ( 21. This is the direction given to reverse the distribution process. When doing this on a quadratic expression, you would use the "box" and "diamond". h e45-144.10 te ely 22. This direction means you should look for a GCF first. 2-e4'n 17K>d Pr 0 pe-e. 23. If two or more numbers are multiplied together and their product is zero, then one of the numbers being multiplied has to be equal to zero. This property is used to solve for x once a quadratic expression is factored. An expression like y like y = (5x +3)(5x-3). 25x2-9 that when factored looks An expression like y = x 2 + 6x + 9 that when factored looks like y (x +3)2 A process used to rewrite a quadratic expression from standard form to graphing/vertex form. CONCEPTS: 1. Factor completely. a. b. 2x2 +7x+ 6 (eix+, 3 (xi z.4 X 2- C. x2-6x + 9 d. 4x2-25 =. K (r2x+* )?.),e-i )
e. x 2 + 4x+1 2x2-8x g. 10x2y + 25xy -15y h. 6x3 + 33x -18x (2-X 2- I- 5x -3) 6Z.X- ix+ -1 2. Equation,--. Graph: Without graphing, state everything you can about the graph given only the equation. a. y=x2 +x-6 tt 's,4_ pa r di* 14- cl-k icz-a,44-11- c to a..,,l,9( A_,eLs e,g,i'vli--e.,e-teot 44 (o, 4) b. y=-(x+2)(x-4) it 's.. plettlibn la --1-LIJ 6 c. 61 CY ),\A tel il PI, Lig C,C -- i IA IL- e.4-7 e pf-s :._4--- i e - 2,, 0) 44.1 No) y (x 1) 2 9 i e 15 el_ olaid A.4 c 4,. vp r kiz,a,..,/- (Ii 3. Equation > Table: Create a table for the given equations. a. y = x 2 + x - 6 & i rt 01, 6.0 14z_ k 1-4da..1 jpe,el s x L-/ - 3 2- - I. - L/ /Li b. Y X 2)(x-4) c. y = (x -1) 2-9. - 44-3 - I o -119 '7 ei 2' ' q - 2-- - ) 0 I "I y /(e -G- - g 5
4. Table Graph: Create a graph for the tables you created in #3. a. y = + x 6 b. y = (x + 2)(x 4) c. y = (x 1) 2 9 5. Graph > Table: Use the graph below to generate a table. x y z- ---7 --1 0-15 -/(# -IS -12-7 q 6. Table Equation: Use the table you created in #5 to identify the key points of the parabola, then generate each type of equation listed. y-intercept: ( vertex: ( x-intercepts: ( Standard Form: GraphingNertex Form: Factored Form: 6C-1) z- (x 4-;)01( X g-' r, 4 X S
Rewrite the following standard form equations in factored form. a. y = 6x 2 -x-2 b. y = 3x 2 +2x -5 1-x Rewrite the following standard form equations in graphing form by completing the square. a. y=x2 6x+7 b. y = x 2-4x -16 X e 3-2- 9. Rewrite the following graphing form equations in standard form. a. y = (x +. 1) 2-4 b. y = (x-2) 2 +7 H
10. Rewrite the following factored form equations in standard form. a. y= (2x+5)(5x-2) b. y = 9(x +2)(x -2) 61.)e- 4- /2)(X- ir) -17A -36 X il DAr - Z:/4O 11. Calculate the x-intercept(s) and y-intercept and vertex for each equation. SHOW ALL WORK! a. y=x2 +4x+3 b. y=5x2-30x 5( (4x-'`"-e-) 1)1 gt.3) 6(.4-1)(Y47,) X 7-./(4 x-intercept(s): ("-/10)(1?) *) x-intercept(s): (bi f) y-intercept(s): it", ; y-intercept(s): ( b i 0) vertex: 61.1 q ) -- I ) vertex: (3 1-i ) tj; f2r- (3) -- 5(1) - qo ---- 5 -el -4/5 4- if
t'r) c. y = (2,x +1)(x -1) 0 = (X -I) 2.)( + 7-0 0 d. y = (x +7)(x -7) r- ()( "l) ex X 4.. 1 o 2_4( X K -It moo", (2-* 0,25 4-1) (0.25 ( - 0.15) br "1-X- x-intercept(s): (--i t 0)( I? ) y-intercept(s): ( 0 1 -i) vertex: (o1-c, /./z) x-intercept(s): (-1 1 6) (7 D) y-intercept(s): (9/ 4/1) vertex: (65-41) e. y = (x+5) 2-25 f. y = -2(x-4)2+32 Z5 X Z' / Me 71 --- 4-5)1. z5 /04 0 2t- =45- $ 25 0= -2 (X-11)2 37- ' 24 ( X -44 )7' LI 7- X 4-4 oe4 t 32 b:--.2y- 1)2451. 14). -214)+3z._ 3z. 17 7- X, X+5 X 4-5 x-intercept(s): (-1 ; o) (01 x-intercept(s): (/o) 0) I vertex: (y-intercept(s): (-51 - ZS) y-intercept(s): vertex: I/ O ' 0 ) 6,/ 3 22' /