Section 5.1 – Graphing Quadratic Functions

•graph quadratic functions

•use quadratic functions to solve real-life problems, such as finding comfortable temperatures

Parabola

Put these graphs into your calculator…

You should see this…

Now Try These…

You should see this…

What does the “a” value in the quadratic form affect about the graph?

Put these into your calculator…

You should see this…

How does the “c” value affect the graph?

Graph of A Quadratic Functiony = ax2 + bx + c

• a > 0• a < 0• │a│< 1• │a│> 1

• x-coordinate of the vertex is –b 2a

• axis of symmetry is the vertical line x = –b 2a

Example 1: Graphing a Quadratic Function

Graph y = 2x2 – 8x + 6

Try the following problems…Pg. 253-254 #20-22

Example 2: Graphing a Quadratic in Vertex Form

Graph y = - (x + 3)2 + 42

1

Try the following problems…Pg. 253-254 #26-28

Example 3: Graphing a Quadratic in Intercept Form

Graph y = – (x + 2)(x – 4)

Try the following problems…Pg. 253-254 #32-34

Example 4: Writing a Quadratic in Standard Form

Write the quadratic function in standard form

a) y = – (x + 4)(x – 9) b) y = 3(x – 1)2 + 8

Try the following problems…Pg. 253-254 #38, 40, 43

Example 5: Using a Quadratic in Standard Form

Researchers conducted an experiment to determine temperatures at which people feel comfortable. The percent y of test subjects who felt comfortable at temperature x (in degrees Fahrenheit) can be modeled by:

y = -3.678x2 + 527.3x – 18,807

Example 6: Using a Quadratic in Standard Form

The Golden Gate Bridge in San Francisco has two towers that rise 500 feet above the road and are connected by suspension cables as shown. Each cable forms a parabola with equation

y =