Graphing Quadratic Functions and Transformations

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 Function The 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-axis Linear 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 Form The 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 Examples For more examples: Watch the video embedded in the course under the notes section for this lesson or go to the following links.

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

Intercept Form The 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.