the function y=-16x²+100 represents the hight y(in feet)

Answered question

2022-04-22

the function y=-16x²+100 represents the hight y(in feet) of a pencil x seconds after falling out the window of a school building. find and interpret the x and y intercepts

Answer & Explanation

nick1337

nick1337

Expert2022-07-31Added 777 answers

y=x2+100

Find the x-intercepts.

To find the x-intercept(s), substitute in 0 for y and solve for x.

0=x2+100

Solve the equation.

Rewrite the equation as x2+100=0.

x2+100=0

Subtract 100 from both sides of the equation.

x2=-100

Take the square root of both sides of the equation to eliminate the exponent on the left side.

x=±-100

Simplify ±-100.

Rewrite -100 as −-1(100).

x=±-1(100)

Rewrite -1(100) as -1100.

x=±-1100

Rewrite -1 as i.

x=±i100

Rewrite 100 as 102.

x=±i102

Pull terms out from under the radical, assuming positive real numbers.

x=±i10

Move 10 to the left of i.

x=±10i

The complete solution is the result of both the positive and negative portions of the solution.

x=10i,-10i

To find the x-intercept(s), substitute in 0 for y and solve for x.

x-intercept(s): NoneNone

Find the y-intercepts.

To find the y-intercept(s), substitute in 0 for x and solve for y.

y=(0)2+100

Remove parentheses.

y=02+100

Remove parentheses.

y=(0)2+100

Simplify (0)2+100.

y=100

y-intercept(s) in point form.

y-intercept(s): (0,100)

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