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How do you find the Vertex of a Parabola?

The Quadratic Formula Equation
\boxed{ ax^2+bx+c = 0 }

has the Vertex Coordinates (h,k) where
\boxed{ h= {-b \over 2a} , k=f( {-b \over 2a }) }

Once computed, (h,k) are plugged into the Vertex Form of a Parabola below.

Vertex Form of Parabola

What is the Vertex of a Parabola?

Every Parabola has either a minimum (when opened to the top) or a maximum (when opened to the bottom).

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

See the illustration of the two vertex locations below.

The Vertical Line passing through the Vertex is the “Axis of Symmetry”: Reflect the one side of the parabola over this axis to obtain the other side the parabola.

Vertex of Parabola

Watch the Video below to find the Vertex Coordinates of a Quadratic Equation:

Example: How do you find the Vertex of the Vertex?

We are given the quadratic equation 3x^2- 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 of the vertex is
(h,k)=(1,-5) .

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

Easy, wasn’t it?

Tip: When using the above Quadratic Vertex Formula to solve
3x^2-6x-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 Quadratic Vertex Formula is y=(x-1)^2-5 .

Get it now? Try the above Quadratic Vertex Formula Calculator a few more times.