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A day full of math games & activities. Find one near you.

A day full of math games & activities. Find one near you.

# What is f(x) = 8x^{2} + 4x written in vertex form?

**Solution:**

Given equation is:

**f(x) = 8x ^{2 }+ 4x --- (i)**

As we know the general equation of the vertex of a parabola is

**y = a(x - h) ^{2 }+ k --- (ii)**

Where (h, k) are the vertices of the parabola

Equating the equation (i) with the general form of the quadratic equation

ax^{2} + bx + c = 0 we get

a = 8, b = 4 , c = 0

Now we know h = b/2a

⇒ h = 4/2(8)

⇒ h = 1/4

Now k = c - (b^{2}) / 4a

⇒ k = 0 - 16 / 32

⇒ k = -1/2

**Now substituting the values of a, h, k in eq(ii) we get the vertex form**

y = 8(x - 1/4)^{2} +(-1/2)

y = 8(x - 1/4)^{2} - 1/2

## What is f(x) = 8x^{2} + 4x written in vertex form?

**Summary:**

The vertex form of the equation f(x) = 8x² + 4x is y = 8(x - 1/4)^{2} - 1/2.

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