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Math  /  Algebra

QuestionIn the following exercise, find the coordinates of the vertex for the parabola defined by the given quadratic function. f(x)=2(x−4)2+3f(x)=2(x-4)^{2}+3
The vertex is □\square (Type an ordered pair.)

Studdy Solution

STEP 1

1. The given quadratic function is in vertex form, which is f(x)=a(x−h)2+k f(x) = a(x-h)^2 + k .
2. The vertex form of a quadratic function directly provides the coordinates of the vertex as (h,k) (h, k) .

STEP 2

1. Identify the vertex form of the quadratic function.
2. Extract the vertex coordinates from the function.

STEP 3

Identify the vertex form of the quadratic function. The given function is:
f(x)=2(x−4)2+3 f(x) = 2(x-4)^2 + 3
This is already in the vertex form f(x)=a(x−h)2+k f(x) = a(x-h)^2 + k .

STEP 4

Extract the vertex coordinates from the function. In the vertex form f(x)=a(x−h)2+k f(x) = a(x-h)^2 + k , the vertex is given by the point (h,k) (h, k) .
From the function f(x)=2(x−4)2+3 f(x) = 2(x-4)^2 + 3 , we can see that:
- h=4 h = 4 - k=3 k = 3
Thus, the vertex is (4,3) (4, 3) .
The vertex is (4,3) \boxed{(4, 3)} .

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