Question

The graph of g is a horizontal stretch by a factor of 2 and a translation 2 units up, followed by a reflection in the y-axis of the graph of
f(x) = 8x^2-6. Write a rule for g. Then identify the vertex.

Answer 1

f(x)=8x^2-6

f(x) = a (x -h)2 + k
horizontal stretch by a factor of 2 -> 1/2 x
2 units up -> k = 2
reflection in y axis -> x value is negative
g(x) = 8*(1/2 x)2 - 6 + 2
g(x) = 2 x2 -4