Question

Using intercepts and the maximum, find an equation for the graph shown.

A)f(x) = 3x2 + 6x - 9

B) f(x) = 3x2 + 6x + 9

C) f(x) = -3x2 + 6x - 9

D) f(x) = -3x2 + 6x + 9




3x2 is 3 the the 2nd power

Answer 1

f(x) = -3x2 + 6x + 9

x-intercepts: x = -1 and x = 3

y-intercept: y = 9

maximum value: y = 12

Answer 2

It's D

Explanation:

The x intercepts ( the zeroes) are -1 and 3 so we can write it as

f(x) = a(x + 1)(x - 3) where a is some constant.

The y intercept is at (0, 9) so substituting:-

9 = a *(0 + 1) * (0 -3)

9 = -3a

a = -3 so we have:-

f(x) = -3(x + 1)(x - 3)

= -3(x^2 - 2x - 3)

= -3x^2 + 6x + 9. (answer)