Examkin

Question

Difficulty: EasyQuadratic Functions and Graphs

The quadratic function ff is defined by f(x)=(x−4)2+7f(x) = (x - 4)^2 + 7. What are the coordinates of the vertex of the graph of y=f(x)y = f(x) in the xyxy-plane?

  1. A
    (−4,7)(-4, 7)
  2. B
    (4,−7)(4, -7)
  3. (4,7)(4, 7)Answer
  4. D
    (7,4)(7, 4)

Answer

The coordinates of the vertex are (4,7)(4, 7).
The quadratic function is given in vertex form, f(x)=a(x−h)2+kf(x) = a(x - h)^2 + k, where the vertex of the graph of the function in the xyxy-plane is (h,k)(h, k). Comparing f(x)=(x−4)2+7f(x) = (x - 4)^2 + 7 to this form, we get h=4h = 4 and k=7k = 7. Therefore, the coordinates of the vertex are (4,7)(4, 7).

Step-by-Step Solution

1
Identify the standard vertex form of a quadratic function.
The vertex form of a quadratic function is f(x)=a(x−h)2+kf(x) = a(x - h)^2 + k, where (h,k)(h, k) is the vertex of the parabola.
This standard form allows direct extraction of the vertex coordinates by matching the variables.
2
Compare the given function f(x)=(x−4)2+7f(x) = (x - 4)^2 + 7 to the standard vertex form.
Comparing the two equations, we identify that a=1a = 1, h=4h = 4, and k=7k = 7.
Matching coefficients and constants determines the values of the vertex parameters.
3
Write the coordinates of the vertex (h,k)(h, k) using the identified values.
The vertex is at (4,7)(4, 7).
Substituting h=4h = 4 and k=7k = 7 into (h,k)(h, k) yields the final vertex coordinates.

Key Concept

Identifying the vertex of a quadratic function from its vertex form.
Rate this question

Topics

Quadratic Functions and Graphs

More questions from this topic