Explain the procedure for graphing the quadratic function in vertex form f(x) = 2(x - 3)2 - 1. Your explanation should show your understanding of using the perfect squares pattern from the vertex.

Answer 1

Vertex form of a parabola is f(x)= a(x-h)^2 +k where the coordinates of the vertex are at (h,k)

and a is our scale factor similar to what slope represents in a linear equation.

So our vertex is at (3,-1)

Since a=2 this parabola will rise twice as fast as a normal parabola.

A change of +1 for x would normally give use a change in y of 1^2 in y in y This would give us the point (4,1)

A change of +2 in x would normally five us a change of 2^2 or 4 for y but we again we have to doulble this to 8 so our next point would be (5,7)

Since parabolas are symmetric about the vertex we get the points (2,1) and (1,7)

Hope this helps