Page 656 - Algebra 1

b. y=x2 -3x-10
SOLUTION
Use a graphing calculator to graph y=x2 -3x-10.
There are two zeros for this function, 5 and -2.
c. y=-2x2-3
SOLUTION
Use a graphing calculator to graph y = -2x2 - 3.
There are no real zeros for this function.
When an object is thrown or kicked into the air, it follows a parabolic path.
S
You can calculate its height in feet after t seconds using the formula
h = -16t2 + vt + s. The initial vertical velocity in feet per second is v, and s is the starting height of the object in feet.
Application: Baseball
A baseball is thrown straight up with an initial velocity of 50 feet per second. The ball leaves the player’s hand when it is 4 feet above the ground. At what time does the ball reach its maximum height?
SOLUTION Substitute the values given for the initial velocity and starting
Math Language
If a quadratic function has no real zeros,
then there are no real numbers that when substituted for x result in y = 0. The graph of such a function does not cross the x-axis.
Example
5
height into the formula h = -16t2 + vt + s. Then find the x-coordinate of
the vertex. Use the formula x = -_b . 2a
h=-16t2 +50t+4 x = - _b
_2a
= - 50 = 1.5625 Substitute values for b and a.
2(-16)
The ball reaches its maximum height 1.5625 seconds after it has been thrown.
Lesson 96 641