Question

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

Answer 1

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`

Answer 2

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)