Answers needed.

Question

Consider the function f(x) = 5x^2-30x +30.

1. What is the vertex of the graph of this function? _______  

1. The maximum/minimum value is  _______.  

The axis of symmetry is  _______.

Answer 1

5x^2-30x+30 = 0

x^2-6x + 6 = 0

x^2 -6x + 9 = -6 +9

(x-3)^2 = 3

x-3 = sqr3

x = 3 + or - sqr3 = x intercepts

x-3 is the axis of symmetry

y= 5(x^2-6x+6) = 5(x-3)^2 +30-45 = 5(x-3)^2 -15

y=a(x-h)^2+k where (h,k) = vertex = (3,-15)

vertex is (3,-15) which is also the minimum point on the parabola

f(x) = 5x^2 -30x + 30

take the derivative and set equal to zero to solve for the minimum point

f'(x) = 10x -30 = 0

10x =30

x = 3 = the x coordinate of the minimum point

y=5(3)^2 -30(3) +30 = 45 -90 +30 = -15 = y coordinate of the minimum point

(3,-15)