Question

Need help for a and b

Answer 1

Answer:

$x = 4.45 \\ y=6$

Step-by-step 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.

$x=\frac{-b±\sqrt{b^2-4ac}}{2a}$

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

Plug them in.

$x=\frac{-4±\sqrt{(4^2)-4(-1)(2)} }{2(-1)}$

$x=\frac{-4±\sqrt{16--8}}{-2} \\ \\ x=\frac{-4±\sqrt{24}}{-2} \\ \\ x = 4.45, -0.45$

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.