Question

Need help for a and b

Answer 1

`x = 4.45 \\ y=6`

Explanation:

For part a, we'll be needing to find the vertex.

Convert
`y=-x^2+4x+2` into vertex form by factoring and completing the square.

We'll get...

`y=-(x-2)^2+6`

So the vertex is
`(2,6)`

And therefore, the maximum height will be 6.

Now we can find the zeros to find how far it'll be.

Use the quadratic formula.

`x=(-b±√(b^2-4ac))/(2a)`

`a=-1 \\ b=4 \\ c = 2`

Plug them in.

`x=(-4±√((4^2)-4(-1)(2)) )/(2(-1))`

`x=(-4±√(16--8))/(-2) \\ \\ x=(-4±√(24))/(-2) \\ \\ x = 4.45, -0.45`

Since the x value has to be positive, x ≈ 4.45, so the water will be about 4.45 out when the water reaches pond level.