1. 9-1 The Function with the Equation y = ax²2
1. Graph y = 1.5x
x y y 16 -3 -2 -1 1 2 3
13.5 6
1.5   12 8   4    x B

2. 2. a. Graph y = -1.5x² x y -3 -2 -1 1 2 3 -13.5 -6 -1.5 ( 0,0 ) 3 & 4
4 __ __
-4 __
-8 __
-12 __
-16 __ -3 -2 -1 1 2 3
-13.5 -6
-1.5  x      
b. What quadrant does this graph have points?
3 & 4
c. What are the coordinates of the
vertex of this parabola?
( 0,0 )

3. Special Properties about Parabolas
If y = ax²
a. The _____ is the line of ________
b. The vertex is ____
c. If a>0, then it opens __, & the
vertex is a ____________ (______
point on the graph).
d. If a<0, then it opens ____, & the
vertex is a ____________
(______ point on the graph).
y-axis
symmetry
(0,0) up
minimum value
Lowest
down
maximum value
Highest

4. 9-2 Solving y = ax² G
3. Use your graph in question 1 above. At what points does the graph of y=7 intersect the graph
of y=1.5x² ? 2
Solve 1.5x = 7  +
 x = 7
1.5 2
x 
To check it, graph y=7 on graph 1.

5. Solve the following equations.
4. 4x² = (4n -3)² = 54
x² = 25
√x² = √25
x =  5
(4n – 3)² = 9
√(4n – 3)² = √9
4n – 3 =  3 so
4n – 3 = 3 or 4n – 3 = -3
4n = n = 0
n = 6/ n = 0
n = 1.5

6. d = 16t² 555 = 16t² 16 16 34.6875 = t² √34.6875 = √t² 5.8896… ≈ t
6. A stone is dropped from the 555-foot Washington Monument,
located on the National Mall in Washington, D.C. To determine
how long the stone will be in the air, use Galileo’s equation
d = 16t². In the equation, t is the time in seconds that it takes
a heavier-than air object to fall d feet. Round your answer to the nearest tenth of a second.
d = 16t²
555 = 16t²
= t²
√ = √t²
5.8896… ≈ t
Since t represents
time, the negative
value is extraneous
for this problems,
therefore there is
only one answer.
5.9 sec. ≈ t