In the vertex form f(x) = a(x - h)^2 + k, what does h represent?

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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

In the vertex form f(x) = a(x - h)^2 + k, what does h represent?

Explanation:
In vertex form, the value h tells you the x-coordinate of the vertex. The vertex is at (h, k), and the graph is shifted horizontally by h because the squared term is written as (x − h). If h is positive, the graph moves right; if h is negative, it moves left. The y-coordinate of the vertex is k since f(h) = a(0)^2 + k = k. The axis of symmetry is the vertical line x = h. The leading coefficient a affects the width and direction (up or down) of the parabola, not the vertex itself. For example, f(x) = 2(x − 3)^2 − 5 has vertex at (3, −5) and symmetry line x = 3.

In vertex form, the value h tells you the x-coordinate of the vertex. The vertex is at (h, k), and the graph is shifted horizontally by h because the squared term is written as (x − h). If h is positive, the graph moves right; if h is negative, it moves left. The y-coordinate of the vertex is k since f(h) = a(0)^2 + k = k. The axis of symmetry is the vertical line x = h. The leading coefficient a affects the width and direction (up or down) of the parabola, not the vertex itself. For example, f(x) = 2(x − 3)^2 − 5 has vertex at (3, −5) and symmetry line x = 3.

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