2.10-2.11 Quiz: Friday Midterm: March 11 2.10 Graph y = ax2 + c 2.10-2.11 Quiz: Friday Midterm: March 11

Vocabulary A quadratic function is a nonlinear (not a line) function that can be written in the standard form y = ax2+ bx + c where a ≠ 0 Every quadratic function has a U-shaped graph called a parabola.

Vocabulary The most basic quadratic function in the family of quadratic functions, called the parent quadratic function, is y = x2 X -2 -1 1 2 Y = 4

Parts of a Parabola 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.

Graph y = ax2 The coefficient “a” can stretch or shrink the graph. If “a” is negative then the graph flips upside down. (Or as I like to call it…makes a SAD face)

Example 1: Graph y = 2x2. Compare the graph with the parent function, y = x2. You need to make a table of values. X -2 -1 1 2 Y =

You Try: Graph y = 1/2x2. Compare the graph with the parent function, y = x2. X -2 -1 1 2 Y =

Example 2: Graph y = -3x2. Compare the graph with the parent function, y = x2. You need to make a table of values. X -2 -1 1 2 Y =

Graph y = ax2 + c The constant “c” moves the graph up or down. If “c” is positive it moves the graph up if “c” is negative it moves the graph down.

Example 4: Graph y = x2 + 2. Compare the graph with the parent function, y = x2. You need to make a table of values. X -2 -1 1 2 Y =

You Try: Graph y = x2 – 4. Compare the graph with the parent function, y = x2.

Homework: P. 100 # 1-9all, 16, 17, 20, 21