Verified Answer :

taskmasters

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)

calculista

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

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

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