the axis of symmetry for the function $f(x) = -x^2 - 10x + 16$ is $x = -5$. what are the coordinates of the…

the axis of symmetry for the function $f(x) = -x^2 - 10x + 16$ is $x = -5$. what are the coordinates of the vertex of the graph?\n\n$(-5, 41)$\n$(-5, 56)$\n$(-5, 76)$\n$(-5, 91)$

the axis of symmetry for the function $f(x) = -x^2 - 10x + 16$ is $x = -5$. what are the coordinates of the vertex of the graph?\n\n$(-5, 41)$\n$(-5, 56)$\n$(-5, 76)$\n$(-5, 91)$

Answer

Explanation:

Step1: Identify the x-coordinate of the vertex

The vertex lies on the axis of symmetry, so $x = -5$.

Step2: Substitute the x-value into the function

$$f(-5) = -(-5)^{2} - 10(-5) + 16$$

Step3: Calculate the square of the x-value

$$f(-5) = -(25) - 10(-5) + 16$$

Step4: Multiply the terms

$$f(-5) = -25 + 50 + 16$$

Step5: Sum the values to find the y-coordinate

$$f(-5) = 25 + 16 = 41$$

Answer:

(-5, 41)