Math 154B Name_____________________ Solving Using the Quadratic Formula Worksheet The Quadratic Formula: For quadratic equations: ax 2 bx c 0 , a b b ac x 2 24Solve each equation using the Quadratic Formula. 1. 4 x 211 x 20 0 2. x 25 x 24 0
8. x 23 x 10 09. x 2 x 310. 2 x 22314 x11. x 22 x 4812. 2 x 23918 x13. 5 x 23 x 1 0 14. 5 x 250 x 125Answers:
x 5 x
x 321 4.2x 55 5. 2x 15 6.2x 25 7. , 34x 5 x
x 113 10.2x 73 11. x ,8 x 612.29 3x
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y = − x 2 + 18 x − 75 4) y = − x 2 + 12 x − 10 Graph each equation.
x y −8 −6 −4 −2 2 4 6 8 − − − − 2 4 6 8 6)y = − x 2 − 6 x − 10 x y −8 −6 −4 −2 2 4 6 8 − − − − 2 4 6 8 Identify the min/max value of each. Then sketch the graph.
x y −8 −6 −4 −2 2 4 6 8 − − − − 2 4 6 8
x 2 + 43x − 163x y −8 −6 −4 −2 2 4 6 8 − − − − 2 4 6 8 -1- ©n P 2 h 0 S 1 e 2 e BKSu 9 tSaU XSuoHfCtAwea 4 rRe 2 9 LtLEC 1 .m p aAElOlm 6 rSiPgihLtisO uryefswePrYvQevdy r aMda 4 dlex Qw 5 iWt 3 hw nIdnkf 0 iZnsijtqez 5 AWldg 8 ewbgrVaL 52 E Worksheet by Kuta Software LLC
x y −8 −6 −4 −2 2 4 6 8 − − − − 2 4 6 8
x y −8 −6 −4 −2 2 4 6 8 − − − − 2 4 6 8 Identify the vertex, axis of symmetry, and min/max value of each.
x 2 + 485x − 1145
x 2 + 7
x 2 − x + 9
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x y −8 −6 −4 −2 2 4 6 8 − − − − 2 4 6 8 Min value = −
x y −8 −6 −4 −2 2 4 6 8 − − − − 2 4 6 8 Max value = − Identify the vertex, axis of symmetry, and min/max value of each.
Vertex: ( 9 , −2)Axis of Sym.: x = 9 Min value = −
Vertex: ( 9 , 5 )Axis of Sym.: x = 9 Min value = 5
x 2 + 485x − 1145Vertex: ( 6 , 6 )Axis of Sym.: x = 6 Max value = 6
Vertex: (−5, 4 )Axis of Sym.: x = − Max value = 4
x 2 + 7 Vertex: ( 0 , 7 )Axis of Sym.: x = 0 Max value = 7
Vertex: ( 6 , 8 )Axis of Sym.: x = 6 Min value = 8
x 2 − x + 9 Vertex: ( 2 , 8 )Axis of Sym.: x = 2 Min value = 8
Vertex: (−2, 1 )Axis of Sym.: x = − Min value = 1 -2- Create your own worksheets like this one with Infinite Algebra 2. Free trial available at KutaSoftware Sketching Quadratic EquationsA sketch graph of a quadratic function should illustrate the following:
You DO NOT need to measure out an accurate scale on a sketch graph, as long as you have provided the information listed above. Sketch graphs of the following quadratic equations, showing y-intercepts, roots, and the vertex. a. y x 2 11 x 10 b. y x 2 12 x 32 c. y x 2 6 x 5 d. y x 2 8 x 15 e. y x 2 12 x f. y x 2 5 x g. y x 2 10 x 21 h. y x 2 11 x 10 i. y 2 x 2 13 x 7 j. y 2 x 2 5 x 12 k. l. y x 2 4 x 4 y x 2 6 x 9 g. shape: x 2 y–intercept: (0, – 21) Roots: (3, 0) and (7, 0) Vertex: (5, 4) h. shape: x 2 y–intercept: (0, – 10) Roots: (1, 0) and (10, 0) Vertex: (5, 20). i. shape: x 2 y–intercept: (0, – 7) Roots: (– 7 ,0) and (0 ,0) Vertex at (– 3, – 28) j. shape: x 2 y–intercept: (0, – 12) Roots at (– 4, 0) and (1, 0) Vertex at (– 1, – 15) k. shape: x 2 y–intercept: (0, 4) double zero and Vertex at (2, 0) l. shape: x 2 y–intercept: (0, – 9) double zero and Vertex at (3, 0) 0 5 10 -2 -1 0 1 2 3 4 5 6 7 8 9 10 y x 0 10 20 -5 0 5 10 15 x y 0 5 10 15 20 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 x y -16- -8- 04 8 12 -6 -4 -2 0 2 4 y x |