For the function f(x) = -x^2 + 6x, find the x-coordinate of the vertex. (2022)

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Question: For the function f(x) = -x^2 + 6x, find the x-coordinate of the vertex. (2022)

Options:

Correct Answer: 3

Exam Year: 2022

Solution:

The vertex x-coordinate is found using x = -b/(2a) = -6/(-2) = 3.

For the function f(x) = -x^2 + 6x, find the x-coordinate of the vertex. (2022)

For the function f(x) = -x^2 + 6x, find the x-coordinate of the vertex. (2022)

Step 1: Identify the coefficients a and b from the function f(x) = -x^2 + 6x. Here, a = -1 and b = 6.
Step 2: Use the formula for the x-coordinate of the vertex, which is x = -b/(2a).
Step 3: Substitute the values of b and a into the formula: x = -6/(2 * -1).
Step 4: Calculate the denominator: 2 * -1 = -2.
Step 5: Now, substitute this value back into the equation: x = -6 / -2.
Step 6: Simplify the fraction: -6 divided by -2 equals 3.
Step 7: Therefore, the x-coordinate of the vertex is 3.

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