Algebra # Standard Form of a Quadratic Function

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Next, press the button to find the Vertex and Vertex Form with Steps.

The Quadratic Equation in Standard Form is

ax²+bx+c = 0 }

Then, the Vertex

h= {-b \over 2a} , k=f( {-b \over 2a }) }

Once computed, the vertex coordinates are plugged into the Vertex Form of a Parabola, see below.

The Vertex is just that particular point on the Graph of a Parabola.

See the illustration of the two possible vertex locations below:

We are given the Standard Form **y=3x²- 6x-2 **.

First, compute the x-coordinate of the vertex **h={ - b \over 2a}= { -(-6)\over (2*3)} = 1 **.

Next, compute the y-coordinate of the vertex by plugging -1 into the given equation: **k= 3*(1)²-6(1)-2=-5 **.

Therefore, the vertex is **(h,k)=(1,-5) **.

Thus, we transformed the above Standard Form into the Vertex Form **y=(x-1)²-5 ** .

Easy, wasn't it?

Tip: When using the above Standard Form Calculator to solve

**3x²-6x-2=0 **we must enter the 3 coefficients as **a=3, b=-6** and **c=-2**.

Then, the calculator will find the Vertex **(h,k)=(1,-5) ** step by step.

Finally, the vertex form of the Parabola is **y=(x-1)²-5 ** .

Get it now? Try the above Standard Form Calculator again.

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