Graphing Quadratic

Functions and Transformations

Linear FunctionThe equation of a linear function looks like

Properties of Quadratic Functions

Quadratic Functions are U-shaped called a Parabola

Quadratic Functions are Symmetrical about the Axis of Symmetry

Quadratic Functions have a vertex (The vertex is a minimum if it’s the lowest point on the parabola and a maximum if it’s the highest point on the parabola.)

The vertex is ALWAYS located on the Axis of Symmetry

Quadratic FunctionThe equation of a Quadratic function looks like one of the following:

How many times did a linear function touch the x-axis? How many times did the quadratic touch the x axis?

Intersecting the x-axisLinear Functions can only intersect the x-axis 1 time (Unless it’s the function y = 0 and then it intersects the x-axis everywhere because it is on the x-axis)

Since Quadratic Functions are u-shaped. The function can intersect the x-axis 0 times, 1 time, or 2 times.

3 Different Forms of Quadratic Functions

We will discuss these forms in the next few slides.

Standard FormThe standard form of a quadratic function is

“a” determines if the parabola is opened up or down

The Axis of Symmetry is the vertical line

The vertex is a point (x, y) at

The y intercept is found by putting 0 in for x and solving for y f(0) = y-intercept (in standard form the y-intercept is always the “c” value)

The x-intercepts are found by putting 0 in for y and solving for x. f(x)=0 (In this lesson we will find these using a calculator)

Standard Form Example

Standard Form Example cont.

Standard Form ExamplesFor more examples: Watch the video embedded in the course under the notes section for this lesson or go to the following links.

Vertex FormThe vertex form of a quadratic function is

“a” determines of the parabola is opened up of down

The Axis of Symmetry is the vertical line x=h

The vertex is a point (x, y) at ( h , k )

The y intercept is found by putting 0 in for x and solving for y f(0) = y-intercept

The x-intercepts are found by putting 0 in for y and solving for x. f(x)=0 (In this lesson we will find these using a calculator)

Vertex Form Example

Vertex Form Example cont.

Vertex Form ExamplesFor more examples: Watch the video embedded in the course under the notes section for this lesson or go to the following links.

Intercept FormThe vertex form of a quadratic function is

“a” determines of the parabola is opened up of down

The Axis of Symmetry is the vertical line that is between the values of x = f and x = g

The vertex is a point (x, y) that is on the axis of symmetry.

The y intercept is found by putting 0 in for x and solving for y f(0) = y-intercept

The x-intercepts are x=f and x=g which will be (f,0) and (g,0)

Intercept Form Example

Intercept Form Example cont.