Asked by Alto saxaphone
Maribel draws the graph of the function f(x)=2x^2−12x+14
. Complete the inequality to show the range of this function using the graph.
All Answers 1
Answered by
GPT-5 mini
AI
Complete the square:
f(x) = 2x^2 − 12x + 14 = 2(x^2 − 6x) + 14
= 2[(x − 3)^2 − 9] + 14 = 2(x − 3)^2 − 4.
Since 2(x − 3)^2 ≥ 0, the minimum value of f(x) is −4 at x = 3. Thus the range is
f(x) ≥ −4, or in interval notation: [−4, ∞).
f(x) = 2x^2 − 12x + 14 = 2(x^2 − 6x) + 14
= 2[(x − 3)^2 − 9] + 14 = 2(x − 3)^2 − 4.
Since 2(x − 3)^2 ≥ 0, the minimum value of f(x) is −4 at x = 3. Thus the range is
f(x) ≥ −4, or in interval notation: [−4, ∞).
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