y = -16x^2 + 18x + 5. y = 1.5x . (1.Find the solutions to the system of linear and quadratic equations. (2. Is one of the solutions unreasonable? Why or why not

Question

A basketball is thrown toward a hoop, with the motion modeled by the function y = -16x^2 + 18x + 5. The height of a nearby hill is modeled by the linear function y = 1.5x .

Answer 1

Solving a "system of equations" means you are looking for the point or points that comply to both equations. That would mean the y-value of one equation would equal the y-value of the other equation so, since y = -16x² + 18x + 5 and also y = 1.5x then:

-16x² + 18x + 5 = 1.5x

-16x² + 16.5x + 5 = 0

Using the quadratic formula:

x = [-b ± √(b² - 4ac)]/(2a)

x = [-16.5 ± √(16.5² - 4(-16)(5))]/((2)(-16))

x = [-16.5 ± √592.25]/(-32)

x = [-16.5 ± 24.336]/(-32)

x = -0.245 and x = 1.276

Often times negative answers are discarded because they may not make sense in real world situations. I'm not sure what a negative in this situation means - the problem seems a bit vague.