Question

what is the \\(y\\)-value of the vertex of the function \\(f(x)=-(x+8)(x-14)\\)?

3
6
112
121

Explanation:

Identify the x-intercepts of the function

The given quadratic function is in intercept (or factored) form:

$$f(x) = -(x + 8)(x - 14)$$

The x-intercepts occur where \(f(x) = 0\). Setting each factor to zero gives:

$$x + 8 = 0 \implies x = -8$$

$$x - 14 = 0 \implies x = 14$$

Find the x-coordinate of the vertex

The x-coordinate of the vertex, \(h\), lies exactly halfway between the two x-intercepts due to the symmetry of the parabola:

$$h = \frac{-8 + 14}{2}$$

$$h = \frac{6}{2} = 3$$

Calculate the y-value of the vertex

To find the y-value of the vertex, \(k\), substitute the x-coordinate \(x = 3\) back into the original function:

$$k = f(3) = -(3 + 8)(3 - 14)$$

$$k = -(11)(-11)$$

$$k = -(-121) = 121$$

The y-value of the vertex is \(121\).

Answer:

• 3
• 6
• 112
• 121 (Correct answer)