Vertex Form of a Parabola # VERTEX TO STANDARD FORM CALCULATOR

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y=a(x-h)²+kwhere

The Standard form of a Parabola is

y=ax²+bx+c

we first apply the binomial formula to expand and get

Next, we distribute the 2 to get

With 2-5=-3 we finally arrive at the Standard Form:

In general, we obtain the Standard Form from the Vertex Form by using these 2 steps:

Given:

Step1: (Use Binomial Formula)

Step2: (Distribute and Combine 2 like terms ah² and k)

..

..

See the illustration of the two possible vertex locations below:

We are given the quadratic equation in vertex format ** y=-2(x+3)²-7 **

First, apply the binomial formula ** (x+3)² = x²+6x+9 **

Thus we have **y= -2(x²+6x+9)-7 **

Next, distribute the 2 to get **y= -2x²-12x-18-7 **

Since -18-7=-25 we finally get the standard form

**y= -2x²-12x-25**

Here, **a=-2, b=-12** and **c=-25** are the coefficients in the Standard Form **y= ax²+bx+c **

Get it now? Try our Vertex to Standard Form Calculator a few more times.

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