Modeling Height of Bouncing Ball

Cuc Chim
Pd. 6
Pre-Calc

2. y = a(x – h)2 + k a= -4.99 h=1.095 k=0.826 x=0.688 y=0 y= -4.99(x-1.095)2+0.826

3. If “a” value changes the graph gets wider. “a” would also change the direction the parabola faces. For example, if it were positive it would face up and if it were negative, it would face down. If “h” value changes, the graph can either move left or right. Meaning the graph shifts horizontally. If the value of “k” changes, the graph gets taller or smaller. Meaning “k” causes the graph to shift vertically.

4. y= -4.99(x-1.095)2+0.826 y=-4.99(x2 -2.19x+1.199)+0.826 y=-4.99x2 +10.9x-5.98+0.826 y=-4.99x2 +10.9x-5.154

5. y=-4.97x2 +10.91x-5.16 Compared to the standard quadratic form found in #4, the value of “a” is smaller than my equation. Its value for “b” and “c” is larger than my model equation.

6. y=-4.97x2+ 10.91x-5.16 y=-4.97(-4.97x2+10.91x-5.16-4.97) y=-4.97(x2- 2.20+1.04) y=-4.97(x2- 2.20x +1.04) y=-4.97(x2- 2.20x+(-2.202)2-(2.202)2+1.04) y=-4.97(x- 2.202)2-(2.202)2+1.04) y=-4.97((x- 2.20)2-.17) y=-4.97((x- 2.20)2+.84)

Compared to the original vertex model in #2, it’s “a” value is smaller by .02. It’s “h” value is about 1.105 more than #2 model. The “k” value is .014 more than #2 model.