Chapter ISG, Problem 9.8.2.3P

a.

To determine

To find: A quadratic function that models the motion of the golf ball and tell what each variable represents.

Answer to Problem 9.8.2.3P

Quadratic function is $y=-16x^2+64x$ , where $x$ represents the time (in seconds) since golf ball is hit and $y$ represents the height of golf ball (in ft).

Explanation of Solution

Given Information: A table containing data-values.

Calculation:

Using quadratic regression feature of the calculator,

  

  $\Rightarrow$ Quadratic function: $y=-16x^2+64x$

In the term $a{x}^2$ , the sign of $a$ determines the direction of the parabola, positive value means that parabola opens upward and negative value signifies that parabola opens downward. In this context it means that first height of golf ball increases over time and then decreases.

In the term $bx$ , $b$ helps in determining axis of symmetry and turning point of a parabola, in this context, it affects the maximum height of the golf ball.

Thus, quadratic function is $y=-16x^2+64x$ , where $x$ represents the time (in seconds) since golf ball is hit and $y$ represents the height of golf ball (in ft).

b.

To determine

To explain: The meaning of constant term in the quadratic function in the context of the problem.

Answer to Problem 9.8.2.3P

When time is $0$ , height of golf ball is also $0$ because golf ball has not been hit yet.

Explanation of Solution

Given Information: Function is $y=-16x^2+64x+0$ .

  $y=-16x^2+64x+0$

Yes, function has a constant term $0$ which corresponds to the $c-value$ . Value of $c$ simply represents $y-\mathrm{int}ercept$ , in this case, it implies that when time is $0$ height of golf ball is also $0$ because golf ball has not been hit yet.

Thus, when time is $0$ height of golf ball is also $0$ because golf ball has not been hit yet.