Question

What is f(x) = 8x2 + 4x written in vertex form?

Answer 1

The equation is a quadratic equation, and it represents a parabola, opening upward. The standard form of this parabola is (x – h)^2 = 4a (y – k) f(x) = y = 8( x^2 + (1/2)x) y + ½ = 8( x^2 + (1/2)x + 1/16) (1/8)(y + ½) = (x + ¼)^2 Vertex is at (-1/4, -1/2)

Answer 2

we have

$f(x)=8x^{2} +4x$

Let

$y=f(x)$

$y=8x^{2} +4x$

Factor the leading coefficient

$y=8(x^{2} +0.5x)$

Complete the square. Remember to balance the equation by adding the same constants to each side

$y+0.5=8(x^{2} +0.5x+0.0625)$

Rewrite as perfect squares

$y+0.5=8(x+0.25)^{2}$

$f(x)=8(x+0.25)^{2}-0.5$------> equation in vertex form

therefore

the answer is

$f(x)=8(x+0.25)^{2}-0.5$