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

Solution:

Given equation is:

f(x) = 8x² + 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

ax² + 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 - (b²) / 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

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What is f(x) = 8x² + 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.