Question

The graph, of quadratic function f has x-intercepts of (-7,0)and(-4,0).

Which equation could represent function f?

A. f(x) = (x-7)(x-4)
B. f(x) = 2(x+7)(x-4)
C. f(x) = -3(x+7)(x+4)
D. f(x) = -1/2(x-7)(x+4)

Answer 1

C. f(x)=-3(x+7)(x+4)

Explanation:

Got it right on the test

Answer 2

C. f(x)=-3(x+7)(x+4)

Explanation:

x-intercept means the value of x where the functions touches the x axis.

The function touches x axis at two places, x=-7 and x=-4 ie. both -7 and -4 are the roots of the equation.

And the terms (x+7) and (x+4) are the factors of the function f(x),

Only one such case exists where (x+7) and (x+4) are there as factors, ie. Option C.

Therefore, C.-3(x+7)(x+4).