Question

date:
2.6 (b) independent practice & hw

1. natalya lisovskaya set the womens shot put world record of 22.6 meters. her throw can be modeled by a quadratic function. suppose the shot put is launched from 1.6 meters off the ground at a velocity of 13.7 meters per second.

a. write a function to represent this situation.
b. what is the initial height of the shot?
e. how long is the shot in the air?
c. how long does it take for the shot to reach its maximum height?
d. what is the maximum height reached by the shot?

1. given the quadratic function $f(x) = 2x^2 - 4x - 16$, find the following features to sketch an accurate graph.

• $y$-intercept
• axis of symmetry
• $x$-intercept(s)/solution(s)
• vertex

1. given the quadratic function $f(x) = -3x^2 - 6x + 13$, find the following features to sketch an accurate graph.

• $y$-intercept
• axis of symmetry
• $x$-intercept(s)/solution(s)
• vertex

Explanation:

Answer:

1. a. \( h(t)=-4.9t^{2}+13.7t + 1.6 \)

b. \( 1.6 \) meters
c. \( t=\frac{-b}{2a}=\frac{-13.7}{2\times(-4.9)}\approx1.4 \) seconds
d. \( h(1.4)=-4.9\times(1.4)^{2}+13.7\times1.4 + 1.6\approx11.2 \) meters
e. Set \( h(t) = 0 \), \( -4.9t^{2}+13.7t + 1.6=0 \), using quadratic formula \( t=\frac{-13.7\pm\sqrt{13.7^{2}-4\times(-4.9)\times1.6}}{2\times(-4.9)} \), \( t\approx3.0 \) seconds

1. \( y \)-intercept: \( (0,-16) \); \( x \)-intercepts: \( x = 4 \) and \( x=-2 \); Axis of symmetry: \( x = 1 \); Vertex: \( (1,-18) \)
2. \( y \)-intercept: \( (0,13) \); \( x \)-intercepts: \( x=\frac{-(-6)\pm\sqrt{(-6)^{2}-4\times(-3)\times13}}{2\times(-3)}=\frac{6\pm\sqrt{36 + 156}}{-6}=\frac{6\pm\sqrt{192}}{-6}=\frac{6\pm8\sqrt{3}}{-6}= - 1\pm\frac{4\sqrt{3}}{3} \); Axis of symmetry: \( x=-1 \); Vertex: \( (-1,16) \)