9-1: Identifying Quadratic Functions
Example 1: Tell whether each function is quadratic. Explain.
cfw_( 2, 9), ( 1, 2), (0, 1), (1,0), (2,7)
y 10 x 2
Example 2: Use a table of values to graph each quadratic e
9-6: Solving Quadratic Equations by Factoring
Zero Product Property
Example 1: Use the Zero Product Property to solve each equation. Check your answer.
( x 7)( x 2) 0
( x 2)( x)
Example 2: Solve each quadratic equation by factoring. Check your answer.
Example 4: Find the vertex
y .25x 2 2 x 3
Example 5: The graph of f ( x)
.06 x 2 .6 x 10.26 can be used to model the height in meters of
an arch support for a bridge, where the x-axis represents the water level and x represents the
9-4: Transforming Quadratic Functions
Width of a parabola (p.613)
Vertical translation of a parabola (p.615)
Example 1: Order the functions from narrowest graph to widest.
f ( x) 3x 2 , g ( x) .5x 2
f ( x)
x 2 , g ( x)
x , h( x )
Example 2: Comp
9-2 Characteristics of Quadratic Functions
Zero of a function:
Axis of Symmetry:
Example 1: Find the zeros of each quadratic function from its graph. Check your answer.
Example 2: Find the axis of symmetry of each parabola
8-5: Factoring Special Products
If a polynomial is a perfect square trinomial, the polynomial can be factored using a pattern. We discussed
Example 1: Determine whether 4x2
Step 1: Find a, b, then 2ab.
9-5: Solving Quadratic Equations by Graphing
Example 1: Solve each equation by graphing the related function.
2 x 2 18x 0
12 x 18
Example 2: A frog jumps straight up from the ground. The quadratic function f (t )
16t 2 1
9-8 Completing the Square
To complete the square
Example 1: Complete the square to form a perfect square trinomial.
A. x2 + 12x + _
B. x2 5x + _
C. 8x + x2 + _
Solving a Quadratic by Completing the Square
Get the _ alone on one side