Question

What is an equation for a parabola that has x-intercepts of (0,0) and (105,0) and a steepness of 1/3?

Answer 1

x-intercepts of (0,0) and (105,0) , is another way to say it has solutions of x = 0 and x = 105, so then

`\bf \begin{cases} x=0\implies &x=0\\ x=105\implies &x-105=0 \end{cases}\qquad \qquad \implies \stackrel{stretch/shrink\qquad \qquad }{\stackrel{\downarrow }{\cfrac{1}{3}}(x)(x-105)=\stackrel{y}{0}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \cfrac{1}{3}x^2-35x=y~\hfill`