9-1 The Function with the Equation y = ax²

1. Graph y = 1.5x 2 x y-3-2-1 0 1 2 3

13.5 6 1.5 0 1.5 613.5

x

y

1 2 3-3 -2 -1

4

8

12

16

B

2. a. Graph y = -1.5x² x y-3-2-1 0 1 2 3

-13.5 -6 -1.5 0 -1.5 -6-13.5

4 __ __ __ __ -4 __ __ -8 __ __-12 __ __-16 __

2 3x

y

-3 -2

b. What quadrant does this graph have points? 3 & 4c. What are the coordinates of the vertex of this parabola? ( 0,0 )

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)

upminimum valueLowest

downmaximum value

Highest

3. Use your graph in question 1 above. At what points does the graph of y=7 intersect the graph of y=1.5x² ?

Solve 1.5x = 72

1.5 1.5

x =2 7 1.5

x + 2.16

+

To check it, graph y=7 on graph 1.

9-2 Solving y = ax² G

Solve the following equations.

4. 4x² = 100 5. 6(4n -3)² = 54 4 4 x² = 25√x² = √25 x = 5

6 6 (4n – 3)² = 9√(4n – 3)² = √9 4n – 3 = 3 so

4n – 3 = 3 or 4n – 3 = -3 4n = 6 4n = 0 n = 6/4 n = 0 n = 1.5

6. A stone is dropped from the 555-foot Washington Monument,located on the National Mall in Washington, D.C. To determinehow 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 16 16 34.6875 = t²√34.6875 = √t²5.8896… ≈ t

Since t representstime, the negativevalue is extraneousfor this problems,therefore there isonly one answer.

5.9 sec. ≈ t