1. ## quadratic function problem solving

I to solve a problem, I solved 2 out of 3 questions now I'm stuck. Sorry if it's not well written, I translated from french.
During a basketball game, Mary throws the ball in the basket. The trajectory of the ball can be represented by the equation h = -0,078d^2 + 0,92d + 2

question: What is the maximum height the ball can reach

I've tried finding the vortex because that seems to make sense in this context but it gives me an answer like -0,78m. This doesn't make sense because it's negative and in the previous question I found that the initial height of the ball is 2m, the maximum height can't be lower than the initial height.
thanks

2. ## Re: quadratic function problem solving

max height, $h$, occurs at the vertex of the parabola's graph

for $f(x)=ax^2+bx+c$ with $a < 0$, $\implies f_{max} = f\left(-\dfrac{b}{2a}\right)$

3. ## Re: quadratic function problem solving

I suspect you dropped a negative sign somewhere- probably in the leading coefficient, -0.078.

It would help if you showed exactly what you did.

4. ## Re: quadratic function problem solving

$h=-0.078d^2+0.92d+2$

$h'=-0.078×2d+0.92$

$h'=0=-.156d+0.92$

$d=\dfrac{0.92}{1.56}$

$d=\dfrac{92}{156}=\dfrac{46}{78}=\dfrac{23}{39}$

$h=-0.078(\frac{23}{39})^2+0.92(\frac{23}{39})+2$

$=-0.027+0.54+2$

$=2.52$