The path of a football kicked by a field goal kicker can be modeled by the equation y = –0.04x2 + 1.56x, where x is the horizontal distance in yards and y is the corresponding height in yards. What is the approximate maximum height of the football?

Question

imstuck · Answer

Do you have choices here for the answers?  I am getting that when x is 39 yards, the max height, occurring at that point, is 1521 yards.  Not totally sure if it's right!  I completed the square on the polynomial.

imstuck · Answer

No wait...error in the math...hold on while I fix it.

imstuck · Answer

Ok, here's the deal.  You have to complete the square on that to solve it for x and y.  Mostly y cuz they want the max height.  To complete the square the coefficient in front of the x^2 has to be a 1, so we need to factor out a -.04.  When you do that you get$$y=-.04(x ^{2}-39x)$$Then you halve the 39 (the x term) and square it; then add it in but also subtract it out to keep the equation in balance.$$y=-.04(x ^{2}-39x+380.25-380.25)$$Then remove the -380.25 from the parenthesis.  Here's the tricky part...because it's inside the parenthesis and the -.04 was factored out of it, when you pull it from the parenthesis, you have to bring the -.04 with it.  Because the 380.25 is negative and the .04 is negative, - times - = + so here's the equation now$$y =-.04(x ^{2}-39x+380.25)+.04(380.25)$$

imstuck · Answer

I know this is a lot but we are almost there.  Now what is inside the parenthesis is actually a perfect binomial square so make it reflect that and do the multiplication on the outside of the parenthesis at the same time.$$y=-.04(x-19.5)^{2}+15.2$$That means that when x is 19.5 yards down the field, the ball is at its max height of 15.2 yards.  And that's the answer.  15.2 yards

goformit100 · Answer

Hello, and A Warm Welcome to Open Study!