What is the new equation of the parabola a=1/2?

Question

The parabola defined by the equation f(x)= x^2-6x+13 is shifted 5 units downward. If the new line of symmetry is at x=4,What is the new equation of the parabola a=1/2?

Answer 1

First put the original equation in vertex form:

 

f(x) =(x² - 6x + 9)  + 4

 

f(x) = (x-3)² + 4  so the original vertex is at (3,4)

 

Shifting it down 5 would make the vertex (3,9)

 

The original line of symmetry is x=3, since it is now x=4, the vertex will be (4,9)

 

So the new equation is F(x) = (x-4)² + 9