I'm stuck, could someone me?
a frog is sitting on a stump 15 feet above the ground. it hops off the stump and lands on the ground 6 feet way. during its leap, its height h is given by the equation h= -0.5x^2+0.5x+15 where x is the distance in feet from the base of the stump, and h is height in feet. how far was the frog from the base of the stump when it was 10.92 feet above the ground?

H = -0.5x² + 0.5x + 15 where x = distance from stump and h = height
We want to find the value of x when h = 10.92.
10.92 = -0.5x² + 0.5x + 15
There are many ways to solve a quadratic like this, let's start by subtracting 10.92.
0 = -0.5x² + 0.5x + 4.08
Now we have everything on one side. Let's solve for x.
Since these numbers aren't whole, I wouldn't try to factor/split the middle.
You could either complete the square or use the quadratic formula.

Completing the square
-0.5x² + 0.5x + 4.08 = 0
We need our x² coefficeint to be 1, so let's multiply by -2.
x² - x - 8.16 = 0
Move the constant to the other side.
x² - x = 8.16
Halve the x coefficient -1 to get -0.5, then square it to get 0.25.
Add this to each side.
x² - x + 0.25 = 8.41
Now we have a perfect square trinomial on the left we can factor...
(x-0.5)² = 8.41
Take the square root of each side...
x-0.5 = ±2.9
Add that 0.5 to each side...
x = 0.5±2.9
Of course, the frog can't be a negative distance x from the stump, so we have to take the positive value x = 3.4.

Using the quadratic formula
-0.5x² + 0.5x + 4.08 = 0
I'm going to multiply everything by 100 just to get rid of any decimal points.
-50x² + 50x + 408 = 0
To use the quadratic formula:
The solution to any quadratic ax² + bx + c is .
In this case, a = -50, b = 50, and c = 408. Let's input these into our formula.





Of course, the frog can't be a negative distance x from the stump, so we have to take the positive value x = 0.34.