Author: mark_cameron
Last saved by: Glencoe Mathematics
Company: McGraw-Hill

Lesson 12-2

Example 1 Graph Quadratic Functions
Graph y = –x^2.

To graph a quadratic function, make a table of values, plot the ordered pairs, and connect the points with a smooth curve.

x | –x^2 | y | (x, y)
–2 | –(–2)^2 =	–4 | –4 | (–2, –4)
–1 | –(–1)^2 =	–1 | –1 | (–1, –1)
0 | –(0)^2 =	0 | 0 | (0, 0)
1 | –(1)^2 =	–1 | –1 | (1, –1)
2 | –(2)^2 =	–4 | –4 | (2, –4)

Example 2 Graph Quadratic Functions
Graph y = 2x^2.

To graph a quadratic function, make a table of values, plot the ordered pairs, and connect the points with a smooth curve.

x | 2x^2 | y | (x, y)
–2 | 2(–2)^2 =	8 | 8 | (–2, 8)
–1 | 2(–1)^2 =	2 | 2 | (–1, 2)
0 | 2(0)^2 =	0 | 0 | (0, 0)
1 | 2(1)^2 =	2 | 2 | (1, 2)
2 | 2(2)^2 =	8 | 8 | (2, 8)

Example 3 Graph Quadratic Functions
Graph y = x^2 + 1.

x | x^2 + 1 | y | (x, y)
–2 | (–2)^2 + 1 =	5 | 5 | (–2, 5)
–1 | (–1)^2 + 1=	2 | 2 | (–1, 2)
0 | (0)^2 + 1=	1 | 1 | (0, 1)
1 | (1)^2 + 1=	2 | 2 | (1, 2)
2 | (2)^2 + 1=	5 | 5 | (2, 5)

Example 4 Graph Quadratic Functions
Graph y = –x^2 + 2.

x | –x^2 + 2 | y | (x, y)
–2 | –(–2)^2 +2 =	–2 | –2 | (–2, –2)
–1 | –(–1)^2 + 2 =	1 | 1 | (–1, 1)
0 | –(0)^2 + 2 =	2 | 2 | (0, 2)
1 | –(1)^2 + 2 =	1 | 1 | (1, 1)
2 | –(2)^2 + 2 =	–2 | –2 | (2, –2)

Example 5 Real-World Example
SCIENCE The function h = 40 – 4.9t^2 represents the height (in meters) of a fireworks rocket after t seconds. Graph this function. Then use your graph to estimate the height of the rocket after 2 seconds. 

The equation h = 40 – 4.9t^2 is quadratic, since the variable t has an exponent of 2. 
Time cannot be negative, so use only positive values of t.

t | h = 40 – 4.9t^2 | (t, h)
0 | 40 – 4.9(0)^2 =	40 | (0, 40)
0.5 | 40 – 4.9(0.5)^2 =	38.8 | (0.5, 38.8)
1 | 40 – 4.9(1)^2 =	35.1 | (1, 35.1)
1.5 | 40 – 4.9(1.5)^2 =	29.0 | (1.5, 29.0)
2 | 40 – 4.9(2)^2 =	20.4 | (2, 20.4)
2.5 | 40 – 4.9(2.5)^2 =	9.4 | (2.5, 9.4)

At a time of 2 seconds, the fireworks rocket would be 20.4 meters.