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Chapter 10.1 Notes: Graph y = ax 2 + c Goal: You will graph simple quadratic functions.

A quadratic function is a nonlinear function that can be written in the standard form y = ax 2 + bx + c. Every quadratic function has a U-shaped graph called a parabola. Basic Quadratic Function: Graph of y = x 2

The lowest or highest point on a parabola is the vertex. The line that passes through the vertex and divides the parabola into two symmetric parts is called the axis of symmetry.

Steps to Graph all Quadratic Functions in the Form y = ax 2 + c: 1.Identify the “a” value. If “a” is positive, the parabola will open up. If “a” is negative, the parabola will open down. The bigger the “a” value, the narrower the parabola will be. The smaller the “a” value, the wider the parabola will be.

2. Identify the “c” value. The “c” value is the vertex, either the highest or lowest point on the parabola. 3. Then make a table of values. Using the coordinates of the vertex, pick two x-values less than the vertex and pick two x- values greater than the vertex. 4. Plot the points and graph the parabola.

Ex.1: Graph y = 5x 2. Ex.2: Graph y = x 2 + 5. Ex.3: Graph y = -5x 2 + 1. Ex.4: Graph Ex.5: Graph y = 3x 2 – 6. Ex.6: Graph

Ex.7: Graph y = -x 2 + 2.

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