Here's my question:

Question

Fireworks are to be launched from a platform at the base of a hill. Using the top of the platform as the origin and taking some measurements, it was determined that the cross-section of the slope of one side of the hill is y=4x-12 If the path of the fireworks is y=-x^2+15x, calculate the point where the fireworks will land on the hill. (Show your work - 3 marks)

Here's my work on the question:
-x^2+15x=4x-12
x^2-11-12=0
(x-12)(x+1)=0

Can you please help me with this one. help would be much appreciated!

Answer 1

Looks a lot like my work. But we'll let that go...

Surely you can now solve the equation! If two numbers have a product of zero, one or the other must be zero.

So, either

x-12 = 0 --> x=12
x+1 = 0 --> x = -1

Clearly the solution is x=12. That is, the firework will hit on the hill 12 feet horizontally from where it was shot.

If you want to find the height, then plug that value into either function, since that is where they are equal.