Question

y = a(x − 2)(x + 4)

In the quadratic equation above, a is a nonzero

constant. The graph of the equation in the xy-plane

is a parabola with vertex ( c, d ). Which of the

following is equal to d ?

A) −9a

B) −8a

C) −5a

D) −2a​

Answer 1

d = -9a  vertex ( c, d ) = ( - 1 , - 9a)  if y = a(x − 2)(x + 4)

Step-by-step explanation:

y = a(x − 2)(x + 4)

=> y = a(x² + 2x - 8)

dy/dx = a(2x + 2)

a(2x + 2) = 0

=> 2x + 2 = 0

=> x = - 1

y = a(x - 2)(x + 4)

using x = - 1

=> y = a(-1 - 2)(-1 +  4)

=> y = a(-3)(3)

=> y = -9a

vertex ( c, d ) = ( - 1 , - 9a)

d = -9a

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