Question

A football player punts a ball. The path of the ball can be modeled by the equation
y= -0.004x^2 + x +2.5, where x is the horizontal distance, in feet, the ball travels and y is the height, in feet, of the ball. How far from the football player will the ball land? Round to the nearest tenth of a foot.

Answer 1

@amistre64 could you help?(:

Answer 2

@ganeshie8

Answer 3

@ranga

Answer 4

"y" is the height of the ball.
When the ball lands, the height will be zero.
Set y = 0 in the equation and solve for x.

Answer 5

@ranga okay so i got 0= -0.004x^2 + x +2.5

I don't know how to start to solve for x.?

Answer 6

We need to isolate x. Add 0.004x^2 to both sides. What do you get?

Answer 7

@ranga 0.004x^2= x + 2.5 ?

Answer 8

Oh, I didn't notice the x before. Okay. This is a proper quadratic equation. Bring the x and the 2.5 over to the left hand side. They will change sign when they switch sides.

Answer 9

0.004x^2= x + 2.5
0.004x^2 - x - 2.5 = 0
divide throughout by 0.004. What do you get?

Answer 10

@ranga it would be x^2 - x - 625?

Answer 11

The coefficient of x is -1. That needs to be divided by 0.004 as well. Also, add = 0 at the end.

Answer 12

okay so it would be x^2 - (-250x) - 625 = 0? @ranga

Answer 13

yes. use quadratic formula to solve for x.
brb

Answer 14

@ranga okay. :)

Answer 15

This one does not factor nicely. So you have to use the quadratic formula to find x.

Answer 16

@ranga okay. hold on a sec

Answer 17

@ranga okay so i got
-250 + √250^2-4(1*-625)/2(1)

Answer 18

@ranga and then solved would be x≈2.475488,−252.475488

Answer 19

\[\Large x = \frac{ 250\pm \sqrt{(-250) ^{2} - 4(1)(-625)} }{ 2(1)}\]

Answer 20

Your signs are switched because you had -250 in the formula but it should have been +250.

x ≈ -2.475488 or 252.475488.

Throw away x ≈ -2.475488 (extraneous solution).

So x ≈ 252.475488
They asked you to round the answer to the nearest tenth of a foot.

So x = 252.5 feet.

Answer 21

@ranga okay thank you so much!! <3 lifesaver.

Answer 22

You are welcome.