N.CN.7, A.CED.1, 2, 3, N.Q.2, A.SSE.1,

Transcription

1 Learning Targets: I can solve interpret key features of quadratic functions from different form. I can choose a method to solve, and then, solve a quadratic equation and explain my reasoning. #1 4 For each quadratic function below, determine the x-intercepts, y-intercept, and vertex and draw a graph of the function. Show your work. 1. f(x) = (x 3) g(x) = (3x 6)(x + 4) 3. h(x) = 2x 2 8x k(x) = 6x x

2 5. Which of the following functions are equivalent to f(x) = x 2 4x 12? a. f1(x) = (x 6)(x 2) b. f2(x) = (x 6)(x + 2) c. f3(x) = (x 2) 2 16 d. f4(x) = (x 2) e. f5(x) = (x 4) f. f6(x) = (6 x)(2 + x) #6 8 Below are pairs of quadratic functions. For each pair, compare and contrast the key features of the functions by selecting all statements that apply. 6. A(x) = 2x 2 8x + 10 and B(x) = 2x 2 8x + 14 B(x) has a y-intercept that is 4 units below the y-intercept of A(x) The parabolas B(x) and A(x) open down A(x) has the following transformations: a horizontal shift, a vertical shift, and a stretch A(x) has the following transformations: a horizontal shift, a vertical shift, and a reflection The parabolas B(x) and A(x) have a minimum value The axis of symmetry of B(x) is at y = 6 B(x) has no x-intercepts The vertex of A(x) lies in Quadrant I 7. C(x) = 1 2 x2 6x + 9 and D(x) = 1 2 x2 8x + 9 The parabolas D(x) and C(x) open up C(x) has the following transformations: a horizontal shift right, a vertical shift down, a compression, and a C(x) has the following transformations: a horizontal shift left, a vertical shift down, a compressions, and a C(x) and D(x) have the same vertex C(x) and D(x) have the same y-intercept C(x) has two positive x-intercepts D(x) has two positive x-intercepts D(x) has a minimum value

3 8. F(x) = (x 5)(x 9) and G(x) = (x 5)(x 9) The standard form of F(x) is F(x) = x 2 14x + 45 F(x) and G(x) have the same x-intercepts The y-intercept of G(x) is (0, 45) G(x) has the following transformations: a horizontal shift right, a vertical shift down, and a G(x) has the following transformations: a horizontal shift right, a vertical shift up, and The vertex of F(x) is (7, 4) The vertex of F(x) is (7, 4) The axis of symmetry of both F(x) and G(x) is at x = 7 9. Circle all the zeros of the function: h(x) = x 2 + 2x Suppose a quadratic function has x-intercepts at 4 and 2, has no stretch or reflections, and it is written in the form: M(x) = Ax 2 + Bx + C. Which of the following statements must be true? C = 8 B 2A = 1 B 2 4AC > 0

4 #1 4 For each quadratic function below, determine the x-intercepts, y-intercept, and vertex and draw a graph of the function. Show your work. 18. f(x) = -(x - 3) g(x) = (3x - 6)(x + 4) 20. h(x) = 2x 2-8x k(x) = 6x x 22. Which of the following functions are equivalent to f(x) = x 2-4x 12?

5 g. f1(x) = (x - 6)(x - 2) h. f2(x) = (x - 6)(x + 2) i. f3(x) = (x - 2) 2-16 j. f4(x) = (x - 2) k. f5(x) = (x - 4) l. f6(x) = -(6 - x)(2 + x) #6 8 Below are pairs of quadratic functions. For each pair, compare and contrast the key features of the functions by selecting all statements that apply. 23. A(x) = 2x 2 8x + 10 and B(x) = 2x 2 8x + 14 B(x) has a y-intercept that is 4 units below the y-intercept of A(x) The parabolas B(x) and A(x) open down A(x) has the following transformations: a horizontal shift, a vertical shift, and a stretch A(x) has the following transformations: a horizontal shift, a vertical shift, and a reflection The parabolas B(x) and A(x) have a minimum value The axis of symmetry of B(x) is at y = 6 B(x) has no x-intercepts The vertex of A(x) lies in Quadrant I 24. C(x) = 1 2 x2 6x + 9 and D(x) = 1 2 x2 8x + 9 The parabolas D(x) and C(x) open up C(x) has the following transformations: a horizontal shift right, a vertical shift down, a compression, and a C(x) has the following transformations: a horizontal shift left, a vertical shift down, a compressions, and a C(x) and D(x) have the same vertex C(x) and D(x) have the same y-intercept C(x) has two positive x-intercepts D(x) has two positive x-intercepts D(x) has a minimum value

6 25. F(x) = (x 5)(x 9) and G(x) = (x 5)(x 9) The standard form of F(x) is F(x) = x 2 14x + 45 F(x) and G(x) have the same x-intercepts The y-intercept of G(x) is (0, 45) G(x) has the following transformations: a horizontal shift right, a vertical shift down, and a G(x) has the following transformations: a horizontal shift right, a vertical shift up, and The vertex of F(x) is (7, 4) The vertex of F(x) is (7, 4) The axis of symmetry of both F(x) and G(x) is at x = Circle all the zeros of the function: h(x) = x 2 + 2x Suppose a quadratic function has x-intercepts at 4 and 2, has no stretch or reflections, and it is written in the form: M(x) = Ax 2 + Bx + C. Which of the following statements must be true? C = 8 B 2A = 1 B 2 4AC > 0