9-1: Identifying Quadratic Functions
Quadratic function:
Parabola:
Vertex:
Example 1: Tell whether each function is quadratic. Explain.
cfw_( 2, 9), ( 1, 2), (0, 1), (1,0), (2,7)
y
7x 3
y 10 x 2
9
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)
0
Example 2: Solve each quadratic equation by factoring. Check your answer.
x
Example 4: Find the vertex
y .25x 2 2 x 3
y
3x 2
6x 7
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
distance in
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)
1 2
x , h( x )
2
2x2
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.
y
x2
2x 3
y
x2
8x 16
Example 2: Find the axis of symmetry of each parabola
Example 3:
8-5: Factoring Special Products
If a polynomial is a perfect square trinomial, the polynomial can be factored using a pattern. We discussed
these specialruleneartheendofchapter7.
a2
2ab
b2
Example 1: Determine whether 4x2
why.
Step 1: Find a, b, then 2ab.
9-5: Solving Quadratic Equations by Graphing
Quadratic equation:
Example 1: Solve each equation by graphing the related function.
2 x 2 18x 0
12 x 18
2x 2
4x
2x 2
3
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
1.
2.
3.
4.
5.
6.
Get the _ alone on one side