What is the name of the U-shaped graph of a quadratic function y = ax^2 + bx + c with a ≠ 0?

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Multiple Choice

What is the name of the U-shaped graph of a quadratic function y = ax^2 + bx + c with a ≠ 0?

Explanation:
A quadratic function with a ≠ 0 graphs as a parabola, a U-shaped curve. The sign of a tells how it opens: up if a is positive, down if a is negative. The graph is symmetric about the vertical axis x = −b/(2a), and it has a vertex at x = −b/(2a) with the corresponding y-value f(−b/(2a)). This shape is unique to a parabola among the common conic sections. A hyperbola has two separate branches, a circle is round with constant radius from a center, and an ellipse is an elongated or circular closed curve. The single, smooth U-shaped arc of a quadratic is best described as a parabola.

A quadratic function with a ≠ 0 graphs as a parabola, a U-shaped curve. The sign of a tells how it opens: up if a is positive, down if a is negative. The graph is symmetric about the vertical axis x = −b/(2a), and it has a vertex at x = −b/(2a) with the corresponding y-value f(−b/(2a)). This shape is unique to a parabola among the common conic sections. A hyperbola has two separate branches, a circle is round with constant radius from a center, and an ellipse is an elongated or circular closed curve. The single, smooth U-shaped arc of a quadratic is best described as a parabola.

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