My teacher gave me this problem where I did a long jump and recorded the distance I went. He then asked us the height. My distance was 80 inches so the x-intercepts are $0,0$ and $80,0$. My question Is how can I make a quadratic Equation using only the $x$ intercepts to find height.
[Math] How to find the vertex of a parabola using only $x$ intercepts.
quadratics
Best Answer
You need additional data to find the height.
For example, the parabolas $y=-x^2+80x$ and $y=-2x^2+160x$ both have the $x$-intercepts you specify, but vertices at $(40,1600)$ and $(40,3200)$, respectively.