Answer: the two corresponding points are:
point (-4, 21) and point (4, 4)
Explanation:
We strectch or compress a function horizontally (in the x direction) by multiplying the argument of the function by a constant.
To compress the factor has to be greater than 1.
In this case the factor is 2.
It means that the new function is g(x) = f(2x)
The points given are (-4,5) and (4,-3)
Then the new points are g(-4) = f(-8) and g(4) = f(8).
You need to find the function f(x) to determine f(-8) and f(8).
The function f(x) is determined using the vertex form.
Vertex form: y = A (x - h)² + k
h and k are the coordinates of the vertex.
From the graph the vertex is (2, -4) ⇒ h = 2, k = - 4
⇒ y = A (x - 2)² - 4
Use other point to find A.
Use the point x = 6, y = 0 ⇒ 0 = A (6 - 2)² - 4 = A(4²) - 4 = 16A - 4
⇒ 16A - 4 = 0 ⇒ 16A = 4 ⇒ A = 4 / 16 = 1 /4
⇒ f(x) = (1/4) (x - 2)² - 4.
Now you can calculate the two points:
g(-4) = f(-8) = (1/4) (- 8 - 2)² - 4 = (1/4) (100) - 4 = 21⇒ point (-4, 21)
g(4) = f(8) = (1/4) (8 - 2)² - 4 = (1/4) 36 - 4 = 4 ⇒ point (4, 4)
