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Tonya iofis Accelerated Integrated Algebra 1 3.2 Notes - PURPLE BOOK Graph Quadratic Functions in Vertex and Intercept Form Vocabulary: 1 Vertex Form -y=a(x-h)*+k where the groph is of the yeax® translated horizontally h units and vertically The vertex is (h,k). The axis_of symme positive , the graph opens up. if 2009 fs arabola. units, iS £2h. Tha is te iS daative the ara opens down . gmp p 2. Intercept Form - gatenge pt Feem ¢ yz a(x-p)(x-g) which carl represent a quadratic eNeTION =| t hos at least one x-interce or zeros are and 9. the axis o midpoint of (6,0) and (9,0) found by using, the equotion x= p+q ya ° ~Ypor x-interce f Sree ty is the Example 1 Write the quadratic function in standard form ax* + bx + c. a) y = (x + 1f b) y = -(« - 1) (x+!) (x4!) -(x-l) (x-1) x +h +| ~ (x2 -2x 41) -X% +2x-4 c) y = 2(x + 2) 2(x+2)(x+42) 2(x?+4oc +4) 227% 48x48 d) y = (x + 1) (x - 1) a -atx-L x-1 Accelerated Integrated Algebra 1 3.2 Notes - PURPLE BOOK Graph Quadratic Functions in Vertex and Intercept Form Example 2 Graph the function. Label the vertex and axis of symmetry. a) y = 2(x - 2)(x - 3) b) y= -(x +3 +1 , _,dxis . x= ae ne aann Vertex 63,1) reper (2-2) cs Ce Axis of ws M ! as | i 2-2 (x-3) e-Geayrtl 4:2: 7¢ “22 +6) t (x43)(x22) +1 = 22S +6) Eile $3ut3x +4) +1 = 2 a be + iD 2 iGo bx ttl om SEE cater) = 0 Vertex! =) = SA Frx 26x -F @ (-x-2)(e+ er D Ly = “55 ox eso xa420) d Verkex <= =) G2) 226 y sm _ 10 , He >a qty 7 q Trtoreapts : eats: o Accelerated Integrated Algebra 1 3.6 Notes - PURPLE BOOK Solve Quadratic Equations by Finding the Square Roots Vocabulary: 1, Rationalize a Denominator - The process of eliminating a radical expression in the denominator of a radical expression in the denominator of a fraction by multiplying both the numerator and denominator by an appropriate radical expression. a. To rationalize the denominator Vb of a function, multiply the numerator and denominator by Jb b. To rationalize the denominator a+ Jb of a function, multiply the numerator and denominator by a—Vb . c, To Rationalize the denominator a-Vb of a function, multiple the numerator and denominator by a+b . 2. Conjugates - the expressions nile a and a—Jé where a and b are rational numbers Example 1 Simplify the expression. 7 TG AS a AF 8 ASt4 95432) Visa 9 Wee 9 BaXepg see 135 207 #15 +32 “II NN d) 243-5 _ QS-10 _ 2NS-10 _ ¥3+5 “B-S 3-95 ~" 99 Accelerated Integrated Algebra 1 3.6 Notes - PURPLE BOOK Solve Quadratic Equations by Finding the Square Roots Example 2 Solve the equation. a) -9d? = 243 b) 11y?+3=36 -q -q «3 “8 Ze \- Iy2233 {dt = ce a d=? 35 Tie Bryst]3 2V-5738 2x43) 4d s) 273 4) 3 93 Example 3 Find the values of a for which the equation had two real number solutions. 8 + Q Gov + GOs & ~S oy @OGo + @po 
