The parent function f(x)=x2 is reflected across the x-axis, horizontally stretched by a factor of 3 and translated 2 units down to create function g

Question

Use the description to write a quadratic function in vertex form

Answer 1

To reflect across the x-axis, we negate change signs of function.  To stretch the function horizontally by a factor of 3, multiply f(x) by 1/3.  Then to translate the function 2 units down, we subtract 2 from the result.

 

 

g(x) = -(1/3)x² - 2

 

This is in vertex form.  Vertex form is   g(x) = a(x - h)² + k

 

a = -1/3 

k = 0

h = -2

 

 

If you have a graphing calculator, you can check out the changes that occur from f(x) to g(x).