I am self-studying precalculus on my own. This is a problem from Ron Larson's precalculus 10e
The arch support of a bridge is
modeled by
$y = −0.0012x^2+
300$, where x and y are
measured in feet and the x-axis represents the ground.(a) Use a graphing utility to graph the equation.
(b) Find one x-intercept of the graph. Explain how to
use the intercept and the symmetry of the graph to
find the width of the arch support.
For the first question (a) I graphed it on desmos
And for the second problem my approach was to use the distance formula and the answer was 1000feet. Since I am doing everything all on my own I have no way of knowing if my answer is correct or not.
Can anybody help me with this please?
Best Answer
Your answer is correct. Here is an example of how I would solve the problem.
We begin by finding the $x$-intercepts, using the fact that the $x$-intercepts are the points where $y = 0$ \begin{align} -0.0012x^2 + 300 = y &= 0 \\ 0.0012x^2 &= 300 \\ x^2 = \frac{300}{0.0012} &= 250000 \end{align} One solution to this equation is $x = \sqrt{250000} = 500$, and since we can see that the graph is symmetric around the $y$-axis, we must have that $x = -\sqrt{250000} = -500$ is also a solution. So we get the width of the arch support to be the difference $500 - (-500) = 1000$ feet between these two points, just as you got.