9-1 The Function with the Equation y = ax² 2 1. Graph y = 1.5x x y y 16 -3 -2 -1 1 2 3 13.5 6 1.5   12 8   4    x -3 -2 -1 1 2 3 B

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   -3 -2 2 3     b. What quadrant does this graph have points? 3 & 4 c. 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) up minimum value Lowest down maximum value Highest

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 1.5 1.5  +  x = 7 1.5 2 x  + 2.16 To check it, graph y=7 on graph 1.

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

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 16 16 34.6875 = t² √34.6875 = √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