Ashton designs movie sets. For one scene, he has to hang a banner across an archway that takes the shape of a parabola modeled by the quadratic equation y = −x2 + 6x. The banner is to be hung at an angle defined by the linear equation y − x = 4, as shown in the figure.
Ashton needs to know the how long a banner to order. He can find the length using the distance formula if he knows the points on the archway at which the ends of the banner are to be attached.
Using the graphing method, find the points at which the equation of the angle of the banner will intersect the equation of the archway.

Question

Vocaloid · Answer

It says to use the graphing method, so use a graphing calculator/graphing software like desmos or wolframalpha, etc. to graph the two equations

y = −x^2 + 6x
and
y − x = 4

to see where the two intersection points are