SOLUTION: 1) Given the vertex form of this quadratic equation complete the following tasks: f(x)=(x+3)^2-2 a) If f(x) is shifted three units to the right, shifted up two units, and

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: 1) Given the vertex form of this quadratic equation complete the following tasks: f(x)=(x+3)^2-2 a) If f(x) is shifted three units to the right, shifted up two units, and      Log On


   

Question 1084313: 1) Given the vertex form of this quadratic equation complete the following tasks:
f(x)=(x+3)^2-2
a) If f(x) is shifted three units to the right, shifted up two units, and reflected vertically over the x-axis, what is the new function?
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b) Graph the original parabola and the transformed parabola on the same coordinate graph.
Found 2 solutions by Boreal, MathLover1:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
The vertex is at (-3, -2); change the sign for the x and keep the same sign for the y.
shift it 3 units to the right and 2 units up, it is f(x)=x^2. The vertex is at the origin.
If it is reflected vertically over the x-axis, it is f(x)=-x^2.
graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C%28x%2B3%29%5E2-2%2C-x%5E2%29

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

f%28x%29=%28x%2B3%29%5E2-2
3 needs to be subtracted on the inside;that will a horizontal shift RIGHT 3 unit,
f%28x%29=%28x-3%29%5E2
and 2 need to be added on the outside; this is a vertical shift UP 2 units
f%28x%29=%28x%2B3%29%5E2%2B2
This is a transformation on the basic function f%28x%29+=+x%5E2. If f%28x%29+=+x%5E2 has the negative is on the outside of the function , like this f%28x%29+=-+x%5E2, it means there is a reflection about the x-axis.
so, you will have:
f%28x%29=+-%28x-3%29%5E2%2B2