Pregunta
Find the vertex of the given function. \( f(x)=|x-5|+10 \) The vertex is at \( (\square \) DONE:
Ask by Brewer Smith. in the United States
Feb 28,2025
Solución de inteligencia artificial de Upstudy
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The vertex is at (5, 10).
Solución
The given function is f(x) = |x - 5| + 10. This is in the vertex form for an absolute value function, which is generally written as f(x) = |x - h| + k, where (h, k) is the vertex.
Comparing f(x) = |x - 5| + 10 with the vertex form, we can see that h = 5 and k = 10.
Thus, the vertex of the function is at (5, 10).
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Simplifique esta solución The Deep Dive
The function \( f(x) = |x - 5| + 10 \) is in the vertex form of the absolute value function. The vertex, which is the point where the function reaches its minimum value, is located at \( (5, 10) \). This is because \( |x - 5| \) reaches its minimum of 0 when \( x = 5 \), resulting in the function value \( 0 + 10 = 10 \). To confirm, think of the absolute value as a "V" shape. The point of the "V," or the vertex, will always be where the expression inside the absolute value equals zero. Here, that point is \( x = 5 \), making the vertex \( (5, 10) \) the spot of affection for your graph!
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