Question

NO LINKS!!! URGENT HELP PLEASE!!!! NOT MULTIPLE CHOICE!!!!

2. You go to the pool to hang out with your friends on a hot summer day. You jump off the diving board and your path through the air can be modeled by the equation m(d) = -4d^2 + 5.5d + 7 in meters per second. Use this scenario to answer questions a - c.

a. How far above the pool do you reach on your dive? (round to the nearest meter)

b. How long are you in the air? (Round to the nearest second)

c. How high is the diving board?

Answer 1

a) You will reach 9 meters above the pool.

b) The length of time you are in the air is 2 seconds.

c) The height of the diving board is 7 meters.

Explanation:

Given quadratic equation:

`m(d)=-4d^2 + 5.5d + 7`

Part a

To determine how far above the pool you reach on your dive, find the y-value of the vertex of the given quadratic equation.

The formula for the x-value of the vertex is -b/2a for a quadratic equation in the form y=ax²+bx+c. Therefore, the x-value of the vertex for the given equation is:

`\implies -(5.5)/(2(-4))=0.6875`

To find the y-value of the vertex, substitute d = 0.6875 into the given equation:

`\begin{aligned}m(0.6875)&=-4(0.6875)^2+5.5(0.6875)+7\\&=-1.890625+3.78125+7\\&=1.890625+7\\&=8.890625\\&=9\; \sf m\;(nearest\;meter)\end{aligned}`

Therefore, you will reach 9 meters above the pool (rounded to the nearest meter).

Part b

You will hit the water when your height is zero. Therefore, to find the length of time you are in the air, set the given quadratic equation to zero and solve for d using the quadratic formula.

`\boxed{\begin{minipage}{3.6 cm}\underline{Quadratic Formula}\\\\$x=(-b \pm √(b^2-4ac))/(2a)$\\\\when $ax^2+bx+c=0$ \\\end{minipage}}`

`\implies d=(-5.5 \pm √(5.5^2-4(-4)(7)))/(2(-4))`

`\implies d=(-5.5 \pm √(142.25))/(-8)`

`\implies d=(-5.5 \pm √(142.25))/(-8)`

`\implies d=-0.803357..., \;2.178357...`

As time is positive we can discount the negative solution. Therefore, the length of time you are in the air is 2 seconds (rounded to the nearest second).

Part c

The height of the diving board is the y-intercept of the graph of the equation. The y-intercept is the value of y when x = 0. Therefore, to find the height of the diving board, substitute d = 0 into the equation.

`\begin{aligned}\implies d(0)&=-4(0)^2+5.5(0)+7\\&=0+0+7\\&=7\end{aligned}`

Therefore, the height of the diving board is 7 meters.