The axis of symmetry for y = ax^2 + bx + c is given by which equation?

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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 axis of symmetry for y = ax^2 + bx + c is given by which equation?

Explanation:
The axis of symmetry is the vertical line that passes through the parabola’s vertex. For y = ax^2 + bx + c, the x-coordinate of the vertex can be found by completing the square: y = a[(x + b/(2a))^2] - b^2/(4a) + c, so the vertex occurs at x = -b/(2a). Equivalently, taking the derivative y' = 2ax + b and setting it to zero gives x = -b/(2a). Therefore the axis of symmetry is x = -b/(2a). Remember, it’s a vertical line; a horizontal line like y = something would not be the axis.

The axis of symmetry is the vertical line that passes through the parabola’s vertex. For y = ax^2 + bx + c, the x-coordinate of the vertex can be found by completing the square: y = a[(x + b/(2a))^2] - b^2/(4a) + c, so the vertex occurs at x = -b/(2a). Equivalently, taking the derivative y' = 2ax + b and setting it to zero gives x = -b/(2a). Therefore the axis of symmetry is x = -b/(2a). Remember, it’s a vertical line; a horizontal line like y = something would not be the axis.

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