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f(x) = -x^2 + 4x + 1 To rewrite in vertex form, complete the square: f(x) = -(x^2 - 4x) + 1 f(x) = -(x^2 - 4x + 4 - 4) + 1 f(x) = -(x - 2)^2 + 3 Therefore, the vertex form is y = -(x - 2)^2 + 3. The vertex is at (2, 3), so h = 2 and k = 3. The parabola opens downward, so it has a maximum value. The maximum value occurs at the vertex, so for x = 2. The maximum value is k = 3.

Name: fx x2 4x 1 to rewrite in vertex form complete the square fx x2 4x 1 fx x2 4x 4 4 1 fx x 22 3 therefore the vertex form is y x 22 3 the vertex is at 2 3 so h 2 and k 3 the parabola opens down 94785
Uploaded: 2020-06-03T17:12:38-08:00
Duration: 1 min 7 s
Channel: Charles Carter
Description: fx x2 4x 1 to rewrite in vertex form complete the square fx x2 4x 1 fx x2 4x 4 4 1 fx x 22 3 therefore the vertex form is y x 22 3 the vertex is at 2 3 so h 2 and k 3 the parabola opens down 94785

          f(x) = -x^2 + 4x + 1

To rewrite in vertex form, complete the square:

f(x) = -(x^2 - 4x) + 1
f(x) = -(x^2 - 4x + 4 - 4) + 1
f(x) = -(x - 2)^2 + 3

Therefore, the vertex form is y = -(x - 2)^2 + 3. The vertex is at (2, 3), so h = 2 and k = 3.

The parabola opens downward, so it has a maximum value. The maximum value occurs at the vertex, so for x = 2. The maximum value is k = 3.

Added by Clayton A.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Charles Carter

06/03/2020

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Step 1: The given function is f(x) = -x^2 + 4x + 1. Show more…

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f(x) = -x^2 + 4x + 1 To rewrite in vertex form, complete the square: f(x) = -(x^2 - 4x) + 1 f(x) = -(x^2 - 4x + 4 - 4) + 1 f(x) = -(x - 2)^2 + 3 Therefore, the vertex form is y = -(x - 2)^2 + 3. The vertex is at (2, 3), so h = 2 and k = 3. The parabola opens downward, so it has a maximum value. The maximum value occurs at the vertex, so for x = 2. The maximum value is k = 3.