confused !!!!!!

Question

A hose used by the fire department shoots water out in a parabolic arc. Let x be the horizontal distance from the hose’s nozzle, and y be the corresponding height of the stream of water, both in feet. The quadratic function is y = −0.016x2 + 0.5x + 4.5.

(a) What is the meaning of the 4.5 that appears in the equation in terms of the fire department?

(b) Use a graphing calculator (like desmos.com) to graph this function. Find the stream’s greatest height.

(c) Use the calculator to find the horizontal distance from the nozzle to where the stream hits the ground.

(d) Use the calculator to determine whether the stream will go over a 6-foot high fence that is located 28 feet from the nozzle? Explain your reasoning.

Answer 1

Go ahead and graph the equation as instructed (I used desmos.com). It will be a downward opening parabola. Zoom in so that you are just looking at the portion of the parabola that is above the x-axis, and to the right of the y-axis. That portion of the graph represents the path of the water stream.

Notice that where the stream starts (x=0 ft), the starting height of the stream is 4.5 ft (y=0 ft is the ground).

You can now zoom in on the appropriate parts of the graph, to answer the remaining questions.

Answer 2

Hi love.

Let's use a basic means to solve it and I will explain it too;

a; The meaning of the 4.5 is; the actual height of the stream of water (y) at the point the horizontal distance from the hose’s nozzle is 0 (zero). That is mathematical. x=0, y=4.5. Hence it is the point at which it cut the y-axises.

b. the stream's greatest height is 8.406ft at a horizontal distance of

Below is the graph link;

https://www.desmos.com/calculator/vatraqhkji- I do use desmos.com. the highest point is indicated at the sharp curve.

c. the horizontal distance from the nozzle to where the stream hits the ground; is;

and x=38.456ft at this point y=0ft which is the stream of water hieght.

Calculating let y=0

therefore;

0=−0.016x² + 0.5x + 4.5

Apply the Almighty formula to find x

The value for x_{1 and} x_{2 is the point at which the stream hit the ground advice always takes the positive value since it is a real-life scenario.}

d.Yes. from the graph when y=6ft, x=28ft

That is;

Substitute x=28ft into the equation and find y;

y=-0.016(28)²+0.5(28)+4.5

y=5.993=6ft