Question
the quadratic parent function f was transformed to create g(x) = f(x - 3) + 5. what is the vertex of the graph of g?
a (-3,5)
b (3,5)
c (5,-3)
d (5,3)
a (-3,5)
b (3,5)
c (5,-3)
d (5,3)
Answers
GPT-4o mini
The quadratic parent function is \( f(x) = x^2 \), which has its vertex at the point (0, 0).
The function \( g(x) = f(x - 3) + 5 \) represents two transformations of the parent function:
1. The \( (x - 3) \) indicates a horizontal shift to the right by 3 units.
2. The \( +5 \) indicates a vertical shift upwards by 5 units.
Starting with the vertex of the parent function (0, 0):
- After shifting right by 3 units, the x-coordinate changes from 0 to \( 0 + 3 = 3 \).
- After shifting up by 5 units, the y-coordinate changes from 0 to \( 0 + 5 = 5 \).
Thus, the vertex of the graph of \( g \) is \( (3, 5) \).
The correct answer is **b (3, 5)**.
The function \( g(x) = f(x - 3) + 5 \) represents two transformations of the parent function:
1. The \( (x - 3) \) indicates a horizontal shift to the right by 3 units.
2. The \( +5 \) indicates a vertical shift upwards by 5 units.
Starting with the vertex of the parent function (0, 0):
- After shifting right by 3 units, the x-coordinate changes from 0 to \( 0 + 3 = 3 \).
- After shifting up by 5 units, the y-coordinate changes from 0 to \( 0 + 5 = 5 \).
Thus, the vertex of the graph of \( g \) is \( (3, 5) \).
The correct answer is **b (3, 5)**.