Question

What is f(x) = 8x2 4x written in vertex form? f(x) = 8(x one-quarter) squared – one-half f(x) = 8(x one-quarter) squared – one-sixteenth f(x) = 8(x one-half) squared – 2 f(x) = 8(x one-half) squared – 4.

Answer 1

The vertex form of the quadratic equation, for the vertex points at which the parabola crosses its symmetry is,

$f(x)=8[(x+\dfrac{1}{4})^2]-\dfrac{1}{2}$

What is vertex form of parabola?

Vertex form of parabola is the equation form of quadratic equation which is used to find the coordinate of vertex points at which the parabola crosses its symmetry.

The standard equation of the vertex form of parabola is given as,

$y=a(x-h)^2+k$

Here, (h, k) is the vertex point.

The given quadratic equation in the problem is,

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

To isolate the term $x^2$ , take out the common number 8 from the equation,

$f(x)=8(x^2+0.5x)$

Add and subtract 0.5/2 in the equation as,

$f(x)=8(x^2+0.5x+\dfrac{0.5}{2}-\dfrac{0.5}{2})\\f(x)=8(x^2+0.5x+\dfrac{1}{16}-\dfrac{1}{16})\\f(x)=8[(x+0.25)^2-\dfrac{1}{16}]\\f(x)=8[(x+\dfrac{1}{4})^2]-\dfrac{1}{2}$

The above equation is vertex form of the given quadratic equation. Thus, the option A is the correct option.

Learn more about the vertex form of the parabola here;

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