Question

1. Which of the following best describes how the graph of f can be obtained from the graph of y = 1/x^2? f(x) = 4/x^2
a. vertical stretch by a factor of -4
b. horizontal shift of 4 units to the right
c. reflection over the y-axis, vertical shrink by a factor of 4
d. reflection over the x-axis, vertical stretch by a factor of 4
2. Determine the quadratic function f whose vertex is (3, -2) and passes through (2,1).
I have to type the answer in the form of f(x) = ax^2 + bx + c.
I would gladly appreciate the help.

Answer 1

1. you must have a typo. If f(x) = -4/x^2, then (d). Otherwise, none of the above. (a) would also be technically correct, but we don't usually denote stretching by negative values.

2. You know that

y = a(x-3)^2 - 2
so, plug in your point:
1 = a(2-3)^2 - 2
a = 3

so, y = 3(x-3)^2 - 2
= 3(x^2 - 6x + 9) - 2
= 3x^2 - 18x + 25