# Vertex and Equation of Axis of Symmetry of Quadratic Functions

Given a quadratic function the vertex and equation of axis of symmetry can be calculated by completing the square of this function. But the derivation will be left to your books and other resources. I will just give the formula how to solve this problem easily.

Definition:

Vertex – the vertex of a quadratic function is the turning point of the graph. This is the point at which the quadratic function changes its direction.

Axis of Symmetry – This is the line that divides the graph of quadratic function into two equal parts.

Formula:

Given a quadratic function the vertex can be calculated using the following formula.

,

The equation of axis of symmetry can be solved using the following equation;

or in standard form

**Worked Problem 1:**

Find the vertex and the axis of symmetry of the function .

[toggle title=”Solution:”]

For vertex

Given: a=1 , b=4, c=-3

For *h*:

For *k*:

For axis of symmetry:

or [/toggle]

**Worked Problem 2:**

The vertex of function is (1,2). What is/are the value/s of *a* and *b*?

[toggle title=”Solution:”]

Using the vertex formula;

equation 1

equation 2.

Using equation 1 and 2:

&

Equating a for both equations we have

Solving for a;

[/toggle]

**Worked Problem 3:**

For what values of b so that the vertex of the function is above the line ?

[toggle title=”Solution:”]

The vertex of is (3/2, -1/4).

Substitute this to y = 2x + b to get -1/4 = (2)(3/2) + b and b = -13/4

Now the question asked for values of b that will make the vertex above the line, and any value of b less than -13/4 will satisfy, thus the answer is b < -13/4[/toggle]

### Dan

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