For a quadratic in standard form ax^2 + bx + c, the axis of symmetry is:

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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

For a quadratic in standard form ax^2 + bx + c, the axis of symmetry is:

Explanation:
The axis of symmetry for a parabola is the vertical line that passes through its vertex. For the quadratic y = ax^2 + bx + c, you can see this by completing the square: y = a[x^2 + (b/a)x] + c = a[(x + b/(2a))^2 - (b/(2a))^2] + c = a(x + b/(2a))^2 + [c - b^2/(4a)] The vertex occurs where the squared term is zero, which is at x = -b/(2a). Since the axis of symmetry is the vertical line through the vertex, it is x = -b/(2a). The other expressions don’t equal this x-coordinate in general, so they don’t describe the symmetry line.

The axis of symmetry for a parabola is the vertical line that passes through its vertex. For the quadratic y = ax^2 + bx + c, you can see this by completing the square:

y = a[x^2 + (b/a)x] + c

= a[(x + b/(2a))^2 - (b/(2a))^2] + c

= a(x + b/(2a))^2 + [c - b^2/(4a)]

The vertex occurs where the squared term is zero, which is at x = -b/(2a). Since the axis of symmetry is the vertical line through the vertex, it is x = -b/(2a). The other expressions don’t equal this x-coordinate in general, so they don’t describe the symmetry line.

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