Consider the function f(x)=-3x^2+30x-9

Answer 1

It's a downward opening parabola, due to the negative coefficient of the x^2 term

y = -3x^2 + 30x -9

complete the square to find the vertex

y = -3(x^2 -10x) -9

take half the coefficient of x and square it to get 25, add 3 times 25 and subtract 3 times 25

y =-3(x^2 -10x +25) -9 +3(25)

y = -3(x-5)^2 +75

y-75 = -3(x-5)^2

this is in the general form of y-h = a(x-k)^2 where (h,k) is the vertex (5,75) and a =-3

the vertex and maximum point is (5,75)

the line of symmetry is x=5

the y intercept is -9

the x intercepts are x=5 +sqr22 or about 0.3 and 9.7