The x-coordinate of the vertex of y = ax^2 + bx + c is given by which expression?

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Prepare for the Praxis Middle School Mathematics Exam with quizzes. Study with flashcards and multiple choice questions. Each question provides hints and detailed explanations. Ensure success on your test!

Multiple Choice

The x-coordinate of the vertex of y = ax^2 + bx + c is given by which expression?

Explanation:
The x-coordinate of the vertex comes from where the parabola centers or where its axis of symmetry lies. For y = ax^2 + bx + c with a ≠ 0, you can see this by completing the square: y = a(x + b/(2a))^2 + (c - b^2/(4a)). The squared term is centered at x = -b/(2a), so that is the x-coordinate of the vertex. You can also get the same result by calculus: the derivative is dy/dx = 2ax + b, and setting it to zero gives x = -b/(2a). Therefore, the x-coordinate of the vertex is -b/(2a).

The x-coordinate of the vertex comes from where the parabola centers or where its axis of symmetry lies. For y = ax^2 + bx + c with a ≠ 0, you can see this by completing the square: y = a(x + b/(2a))^2 + (c - b^2/(4a)). The squared term is centered at x = -b/(2a), so that is the x-coordinate of the vertex. You can also get the same result by calculus: the derivative is dy/dx = 2ax + b, and setting it to zero gives x = -b/(2a). Therefore, the x-coordinate of the vertex is -b/(2a).

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