Parabola Basics

Front

What is a parabola?

Back

A parabola is a U-shaped curve that is the graph of a quadratic function. It can open upwards or downwards.

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What is the vertex of a parabola?

Back

The vertex is the highest or lowest point on the parabola, depending on its direction. It is the point where the parabola changes direction.

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What is the y-intercept of a parabola?

Back

The y-intercept is the point where the parabola crosses the y-axis. It occurs when x=0.

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What is the x-intercept of a parabola?

Back

The x-intercept(s) are the points where the parabola crosses the x-axis. They occur when y=0.

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How do you find the vertex of a parabola given its equation in standard form?

Back

For a parabola in the form y = ax^2 + bx + c, the vertex can be found using the formula x = -b/(2a).

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What does the 'a' value in the quadratic equation indicate about the parabola?

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The 'a' value determines the direction of the parabola (upward if a > 0, downward if a < 0) and its width (larger |a| means narrower, smaller |a| means wider).

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What is the axis of symmetry in a parabola?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves. It passes through the vertex.

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What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax^2 + bx + c.

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How can you identify a parabola from a set of graphs?

Back

A parabola can be identified by its U-shape and the presence of a vertex. It may open upwards or downwards.

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What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b^2 - 4ac) determines the number of real roots of the quadratic equation: if > 0, two real roots; = 0, one real root; < 0, no real roots.