what is the $x$-intercept of the graph of the function $f(x) = x^2 - 16x + 64$?

$(-8, 0)$
$(0, 8)$
$(8, 0)$
$(0, -8)$

Question

what is the $x$-intercept of the graph of the function $f(x) = x^2 - 16x + 64$?

$(-8, 0)$
$(0, 8)$
$(8, 0)$
$(0, -8)$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": true, "concepts_used": [ "x-intercept of a Line" ], "new_concepts": [ "x-intercept of a Quadratic Function", "Perfect Square Trinomials" ], "current_concepts": [ "x-intercept of a Line", "x-intercept of a Quadratic Function", "Perfect Square Trinomials" ] } ## Define the x-intercept condition Using the *x-intercept of a Line* knowledge point $$ f(x) = 0 $$ ## Set up the quadratic equation $$ x^2 - 16x + 64 = 0 $$ ## Factor the perfect square trinomial $$ (x - 8)^2 = 0 $$ ## Solve for x $$ x = 8 $$ ## Write as a coordinate point $$ (8, 0) $$

(A) $(-8, 0)$

(B) $(0, 8)$

(C) $(8, 0)$

(D) $(0, -8)$

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QUESTION IMAGE

Question

Explanation:

Define the x-intercept condition

Set up the quadratic equation

Factor the perfect square trinomial

Solve for x

Write as a coordinate point

Answer: