Question

Can someone explain how to convert a quadratic function in standard form to vertex form using the "complete the square" method? Oh, please give steps so I can write them down

Answer 1

The required steps are explained below to convert the quadratic function into a perfect square.

What is the parabola?

It's the locus of a moving point that keeps the same distance between a stationary point and a specified line. The focus is a non-movable point, while the directrix is a non-movable line.

Let the quadratic function be y = ax² + bx + c.

The first step is to take common the coefficient of x². We have

$\rm y = a \left (x^2 + \dfrac{b}{a}x \right) + c$

Add and subtract the half of the square the coefficient of x,

$\rm y = a \left (x^2 + \dfrac{b}{a}x + \dfrac{b^2}{4a^2} \right) - a \times \dfrac{b^2}{4a^2} + c$

Then we have

$\rm y = a \left (x + \dfrac{b}{a} \right)^2 - \dfrac{b^2}{4a} + c$

These are the required step to get the perfect square of the quadratic function.

More about the parabola link is given below.

brainly.com/question/8495504

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