Question

Find the vertex : f(x)=3x^2-18x+10

Answer 1

f(x)=3x^2-18x+10

a = 3, b = -18 and c = 10

The vertex of a parabola is in form a(x+d)^2 + e

d = b/2a = -18/2(3) = -18/6 = -3

e = c-b^2/4a = 10 - -18^2/4(3) = 10-27 = -17

Now the vertex form of the parabola becomes 3(x-3)^2 -17

Use the vertex form of the parabola in the vertex form of y = a(x-h)^2 +k

Where a = 3, h = -3 and k = -17

Now you have y = 3(x-(-3))^2 +(-17)

Simplify: y = 3(x+3)^2 -17

The vertex becomes the h and k values of (3,-17)