2.10Graph 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 0 1 2

Y = 4 1 0 1 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 0 1 2

Y =

You Try:

• Graph y = 1/2x2. Compare the graph with the parent function, y = x2. X -2 -1 0 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 0 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 0 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