what is the $y$-value of the vertex of the function $f(x)=-(x-3)(x+11)$?

$\bigcirc$ $-8$
$\bigcirc$ $-4$
$\bigcirc$ $33$
$\bigcirc$ $49$

Question

what is the $y$-value of the vertex of the function $f(x)=-(x-3)(x+11)$?

$\bigcirc$ $-8$
$\bigcirc$ $-4$
$\bigcirc$ $33$
$\bigcirc$ $49$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Intercept Form", "Quadratic Vertex" ], "current_concepts": [ "Intercept Form", "Quadratic Vertex" ] } ## Find the x-intercepts of the quadratic function $$ \begin{aligned} &f(x) = -(x-3)(x+11) \ &x_1 = 3, \quad x_2 = -11 \end{aligned} $$ ## Calculate the x-coordinate of the vertex $$ \begin{aligned} x_v &= \frac{x_1 + x_2}{2} \ x_v &= \frac{3 + (-11)}{2} = \frac{-8}{2} = -4 \end{aligned} $$ ## Evaluate the function at the vertex x-coordinate to find the y-value $$ \begin{aligned} y_v &= f(-4) \ y_v &= -(-4 - 3)(-4 + 11) \ y_v &= -(-7)(7) \ y_v &= 49 \end{aligned} $$

-8

-4

33

49

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Quadratic Vertex" ] }

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QUESTION IMAGE

Question

Explanation:

Find the x-intercepts of the quadratic function

Calculate the x-coordinate of the vertex

Evaluate the function at the vertex x-coordinate to find the y-value

Answer: