What is the vertex of the parabola y = -3(x - 2)^2 + 5?

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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

What is the vertex of the parabola y = -3(x - 2)^2 + 5?

Explanation:
Think about the vertex form y = a(x − h)^2 + k. The vertex is the point (h, k). In y = −3(x − 2)^2 + 5, the values are h = 2 and k = 5, so the vertex is (2, 5). The negative a means the parabola opens downward, but it doesn’t move the vertex. The (x − 2) shows a rightward shift of 2, and the +5 shows an upward shift of 5, placing the peak at x = 2, y = 5. If the vertex were at (-2, 5) or (2, -5) or (-2, -5), the squared term or the constant would have different signs or expressions, which doesn’t match this equation.

Think about the vertex form y = a(x − h)^2 + k. The vertex is the point (h, k). In y = −3(x − 2)^2 + 5, the values are h = 2 and k = 5, so the vertex is (2, 5). The negative a means the parabola opens downward, but it doesn’t move the vertex. The (x − 2) shows a rightward shift of 2, and the +5 shows an upward shift of 5, placing the peak at x = 2, y = 5. If the vertex were at (-2, 5) or (2, -5) or (-2, -5), the squared term or the constant would have different signs or expressions, which doesn’t match this equation.

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