Question

Which equation matches the graph shown below?

A. y = 8x² + 2x – 5
B. y = 8x² + 2x + 5
C. y = 2x² + 8x + 5
D. y = 2x² + 8x – 5

Answer 1

The graph is a parabola with roots at (-4.5, 0) and (0.5, 0) and vertex at (-2, -13)
Equation using roots is a(x + 9/2)(x - 1/2) = a(x^2 + 4x - 9/4) = ax^2 + 4ax - 9/4 a . . . . . . . . (1)
Equation using vertex is a(x + 2)^2 - 13 = a(x^2 + 4x + 4) - 13 = ax^2 + 4ax + 4a - 13 . . . . . . . . (2)
From (1) and (2), -9/4 a = 4a - 13
13 = 4a + 9/4 a = 25/4 a
a = (4 x 13)/25 = 2.08 = 2 approx

Therefore required equation is y = 2x^2 + 4(2)x + 4(2) - 13 = 2x^2 + 8x + 8 - 13 = 2x^2 + 8x - 5

Answer 2

Answer:

1.Which equation represents the axis of symmetry of the function y = –2x² + 4x –6

B. x=1

2.What are the coordinates of the vertex of the graph of the function y = –x² + 6x –11

A. (3, -2)

3.What are the coordinates of the vertex of the graph of the function y = –3x² –12x + 3

D. (-2, 15)

4. Which graph represents the function y=3x^+12x-6

B. second graph

5. which equation matches the graph shown below

D. y = 2x^2 + 8x - 5

6. Which of the following functions has a rate of change that stays the same

B. y = 19x - 10