SOLUTION: Can you please help me find the vertex and factor the equation of y=-16x^2+24x so far for factoring it I have y=-8x(2x-3) but I am not sure if I did that right.

Question 368649: Can you please help me find the vertex and factor the equation of y=-16x^2+24x
so far for factoring it I have y=-8x(2x-3) but I am not sure if I did that right.
Answer by lefty4ever26(59) (Show Source): You can put this solution on YOUR website!
You have it factored right...Set equal to 0 to find x values (there will be 2)
0=-8x(2x-3)
-8x=0 2x-3=0
x=0 and x=3/2 These are the y intercepts and we know from the function that it is an upside down parabola. (because of the -16x^2)
To find the maximum point (which would be the vertex) take the derivative of the function
y=-16x^2+24x
y'=-32x+24 Set equal to 0 and solve for x
-32x+24=0
x=3/4 Plug x=3/4 back into the original function
y=-16(3/4)^2+24(3/4) Solve for y
y=-9+18=9. So your vertex is at the point (3/4,9)

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