Question

The equation f(x) = 4x2 − 16x + 9 represents a parabola. What is the vertex of the parabola? (2, −7) (−2, 57) (4, 9) (−4, −137)

Answer 1

Option A is correct

Vertex = (2, -7)

Explanation:

A quadratic equation is in the form of:

`ax^2+bx+c=0` .....[1]

then;

Axis of symmetry is given by:

`x =(-b)/(2a)`

Vertex =
`((-b)/(2a), f((-b)/(2a))`

As per the statement:

The equation :

`f(x) = 4^2- 16x + 9`

On comparing with [1] we have;

a = 4, b = -16 and c =9

we have;

`x = (-(-16))/(2 \cdot 4) = (16)/(8) = 2`

Substitute x= 2 in f(x) we have;

`f(2) = 4(2)^2-16(2)+9 = 16 - 32+9 = -16+9 = -7`

Vertex = (2, -7)

therefore, the vertex of the parabola is, (2, -7)