Category: Applications

Today’s quiz consisted of several questions centered around finding the area between two curves: \(y=x^2+2x-8\) and \(y = 4-x^2\). The first question asked for the points of intersection for the two curves. By substitution, we arrive at \(x^2+2x-8=4-x^2\) which has solutions \(x=-3\) and \(x=2\). In order to find the points of intersection, we need both \(x\) and \(y\)-coordinates, so for each \(x\) we find the corresponding \(y\). Note that our two \(x\)-values are intersections of the two curves, so both equations should give us the same \(y\)-value when we plug in the same \(x\)-value.