The vertex of f(x) = √(x − h) + k occurs at which point?

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Study for the Algebra 1 Honors End-of-Course Test. Study with flashcards and multiple-choice questions, each question has hints and explanations. Get ready for your exam!

Multiple Choice

The vertex of f(x) = √(x − h) + k occurs at which point?

Explanation:
The main idea here is how shifts move the vertex of a square root graph. The basic graph y = sqrt(x) has its vertex at (0, 0). If you shift the graph right by h, you replace x with x − h, so the vertex becomes (h, 0). Then shifting up by k adds k to the y-coordinate, moving the vertex to (h, k). Since f(x) = sqrt(x − h) + k is exactly these shifts, its vertex sits at (h, k). The domain starts at x = h, which matches the x-coordinate of the vertex. So the vertex is (h, k).

The main idea here is how shifts move the vertex of a square root graph. The basic graph y = sqrt(x) has its vertex at (0, 0). If you shift the graph right by h, you replace x with x − h, so the vertex becomes (h, 0). Then shifting up by k adds k to the y-coordinate, moving the vertex to (h, k). Since f(x) = sqrt(x − h) + k is exactly these shifts, its vertex sits at (h, k). The domain starts at x = h, which matches the x-coordinate of the vertex. So the vertex is (h, k).

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