Page 786 - Algebra 1

Example
2
Application: Baseball
A baseball is thrown in the air with an initial velocity of 20 feet per second from 5 feet off the ground. Use the equation h = -16t2 + 20t + 5 to model the situation. Will the ball reach a height of 30 feet?
SOLUTION
h=-16t2 +20t+5
30 = -16t2 + 20t + 5 Substitute 30 for h.
0 = -16t2 + 20t - 25 Set the equation equal to 0.
Use the discriminant to determine if the ball will reach a height of 30 feet.
b2 - 4ac = 202 - 4(-16)(-25) = 400 - 1600
= -1200
Since the discriminant of the equation is negative, there are no solutions.
The ball will not reach a height of 30 feet.
Use the discriminant to find the number of real solutions to the equation. Then state the number of x-intercepts of the graph of the related function.
Math Reasoning
Generalize What are the values of a, b, and c in the quadratic equation
x2 -4=0?
Lesson Practice
Practice
Distributed and Integrated
a.
(Ex 1)
b.
(Ex 1)
c.
(Ex 1)
d.
(Ex 2)
x2 -2x-35=0 4x2 +20x+25=0 2x2 -3x+7=0
A football is punted from 2 feet off the ground with an initial velocity of 60 feet per second. Use the equation y = -16t2 + 60t + 2 to model the situation. Will the ball reach a height of 45 feet?
*1. Find the value of the discriminant of the equation 3x2 - x + 2 = 0. (113)
2. The new rectangular basketball court at the high school has a width of
(53) 9x2 + x + 36 and a length of 4x2 + 2x + 2. What is the perimeter of the new
court?
3. Solve 6⎢z - 3 = 18.
(74)
4. Find 8!. (111)
Lesson 113 771