( x) ( ) ( ) ( ) Practice: Find the x and y intercepts. Finding the x and y intercepts. Set y = 0 to find x-intercept: Set x = 0 to find y-intercept:

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1 Finding the and y intercepts y + = 8 Set y = to find -intercept: Set = to find y-intercept: y+ = 8 + = 8 = 8 = y+ = 8 y + = 8 y = 8 y = The -intercept is (, ) and the y-intercept is (, ) : Find the and y intercepts. ) y+ = ) 9y = 9./8.EE., F-IF-7a Finding the slope and y-intercept of the line y+ = 8 First solve for y: y+ = 8 y+ = 8 y = 8 y 8 = + y = + ( ) y = Find the slope by identify the coefficient of : m = : Identify the slope & y-intercept ) y = 9 ) y+ = Find the y-intercept by identifying the constant:,./8.ee., F-IF-7a Page of MDC@ACOE (HUSD) /8/

2 Graphing: y + = 8 Method : Find & y-intercept: From eample,, Plot the points and draw the line Method : Make a table of values and plot the points ( ) and : Graph these equations. ) y + 8= ) y = Method : Use slope & y-intercept.,7./a-rei-, F-IF-7a rise change in the y coordinates Slope = = run change in the coordinates Horizontal line: Find the slope of the line m = change in change in = Vertical Line: Find the slope of = y = the line y m = change in change in = = = = Slope is Since division by is not defined, this line has no slope or undefined y : Find the slope 7) (, ), (, ) 8) (, ), (, ) 9) =./8.EE. Page of MDC@ACOE (HUSD) /8/

3 Write the equation of the line with a slope of,. and passing through the point Use the point slope form of a line, m is the, y =, slope and ( ) y y = m( ) y ( ) = ( ) y + = y + = y = Write the equation of each line. ) Find the equation of the line passing, and no slope. through the point ) Find the equation of the line passing through the point (, ) with a slope of. Given y = a + b + c for constants a and b. y = b is a horizontal line with a m = = a is a vertical line with no slope (undefined slope) ) Slope is and passes through the, point ) Passes through the points, and, Finding parallel and perpendicular slopes The slope of line l is which also can be written m =., 7. A line parallel to line l has the same slope so m = m = A line perpendicular to line l has the slope m such that m m = : : Find the slope that satisfies each condition Line m is given by the equation y+ = ) Find the slope of the line parallel to line m ) Find the slope of the line perpendicular to line m. m m m = m m = = = 7.,8./G-GPE. Page of MDC@ACOE (HUSD) /8/

4 Solving systems of equations: Method : Graphing y = Solve the system: y = Graph y= by finding intercepts Draw the line using (, )(, ) Solve the systems by graphing ) y = + y = Graph y = using slope & y-intercept 7) + y = + y = Identify the point of intersection y = (, ) is the solution to y = 9./8.EE.8a Method : Substitution Solve the system: Solve for one variable Eq. + y = + y = + y = y = y = or y = + Substitution- Substitute + for y in Eq. Solve by substitution: 8) + y= + y = Solve for Substitute = for y y = + y = + y = 9+ y = -y = ( ) = + = = (, ) is the solution to the system = = 9. /8.EE.8b 9) + y = + y = Page of MDC@ACOE (HUSD) /8/

5 Method:Solving systems using elimination Solve: y = + y = st Rewrite equations so they have opposite terms. Multiply Eq. by (So y and y are opposite) ( y) = + y= nd Add the equations vertically: rd Solve the equation for. th Solve for y by substitution: + y = + y = + y = Radical Epressions: Simplify 9./8.EE.8b Eample Eample 8m n p y i 8 y Eample y = y = = iiim n n( p ) = m n p n = mnp n = = 8z z 8z z 8 z i = 9z = z y = + y = 7+ y = Eample 7 = = (,) is the solution to the system = i8 y = iiii y = y = y 7 + = 9 + = + = + = +./8.EE., N-RN. Solve the systems by using Elimination ) + y = y = 8 ) A vending machine takes only nickels and dimes. At the end of the day there were three times as many nickels as dimes and a total of $. How many of each coin were there in the machine? ) + 7y = y = Simplify each epression ) 8 p q ) w i w ) 8 r ) Page of MDC@ACOE (HUSD) /8/

6 Solving Radical Equations: 7+ y + = y + = ( y + ) = Isolate the radical Square both sides Check your answer(s)./8.ee.7, N-RN. Solving Quadratic Equations By Factoring y + = ( )( ) y = y = + = + = + = = or + = = or = Use the zero-product property Check your answer(s) By Completing the Square + 8+ = Add - to both sides + 8= + 8+ = + ( ) + = + ( ) + = + =± = ± = + and = = and = Add to both sides to complete the square Square root both sides Simplify radicand Solve 7) = + 9 8) z + = Solve for. If the equation has no solution, write no solution. 9) + = ) ( ) = 9 ) ) ) = + = y + = 8 Finding Square Roots m = m = m m = = ± m = ± m = ± m = ±.,./A-SSe.a, A-REI.b ) y + y = Page of MDC@ACOE (HUSD) /8/

7 Solve the equation by using the quadratic formula: = a =, b=, c= ± = a b b ac ( ) ( ) ± = ± + = ± = ± = ± = Standard form Identify a, b, c Substitute Simplify Solve for : ) ) 7) = + = 7 = 8) + =./A-REI-b Compound Inequalities Solve and Graph Eample ( ) + < + < or + < + > or < > Solve and graph each inequality or equation: 9) z + ) > Eample { < < } Solution Set or or or { } Solutionset or ) y 7 ) < + 7 ) 7 = /A-REI. Page 7 of MDC@ACOE (HUSD) /8/

8 Graphing Quadratics: Graph the function f ( ) = + st Find the verte Find the -coordinate of the verte Graph the functions: g = ) b = a = = ) y = + Find the y-coordinate of the verte by substituting the -coordinate into the equation and solve for y. f f = + ( ) = ( ) + ( ) = + ( ) = verte (, ) nd Make a table of values. Choose points on both sides of the verte y = + y rd Graph the parabola f = + ) 7) y = For #8 & 9, find the domain and range of the relation Is each relation a function? { } 8) (, ), (,), (, ),, 9) y ) What is the range of the function f {,,, }? = + when the domain is 7.,./A-SSe.a,b, F-IF.7a Page 8 of MDC@ACOE (HUSD) /8/

9 Algebra Study Guide Answer Key ) (, );(, ) ) (, ) ) (, );(, ) 7) ( 9, ) ) m =, (, ) 8) (, ) ) ) m =,, 9) 7, ) (, ) ) = 9, = 9 ) =, = ) No Solution ) ) = ± 9 =, = ) ) (, ) ) 7 =, = There are nickels and dimes ) m = ), 7) = ± 8) m = ) pq p 8), 9) No slope, undefined ) w w 9) 9 z z slope ) = ) r ) < or > r ) yy or y y = ) 9 ) { } = = ) { < } ) y= + 7) or ) y = + 8) z = ) m = 9) =, =, or = ) m = ) =, = 9 ) = 8 or = 8 Page 9 of MDC@ACOE (HUSD) /8/

10 ) ) ) 7) ) Domain {,, } Range {,,, } No it is not a function because where =, the equation has two values of y. 9) Domain {,,, } Range {, } Yes it is a function. ) When the domain is {,,, } the range is {7,., } Page of MDC@ACOE (HUSD) /8/