Quadratic Formula

Front

What is the Quadratic Formula?

Back

The Quadratic Formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the solutions (x-intercepts) of a quadratic equation ax² + bx + c = 0.

Front

What does the discriminant (b² - 4ac) indicate?

Back

The discriminant determines the number of real solutions of a quadratic equation: if > 0, there are 2 solutions; if = 0, there is 1 solution; if < 0, there are no real solutions.

Front

How many x-intercepts does a parabola with a positive discriminant have?

Back

A parabola with a positive discriminant has 2 x-intercepts.

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How many x-intercepts does a parabola with a discriminant of zero have?

Back

A parabola with a discriminant of zero has 1 x-intercept.

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How many x-intercepts does a parabola with a negative discriminant have?

Back

A parabola with a negative discriminant has no x-intercepts.

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What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

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What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on whether it opens upwards or downwards.

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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, given by the formula x = -b/(2a).

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What does it mean for a quadratic function to open upwards?

Back

A quadratic function opens upwards if the coefficient of x² (a) is positive, indicating that the vertex is the minimum point.

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What does it mean for a quadratic function to open downwards?

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A quadratic function opens downwards if the coefficient of x² (a) is negative, indicating that the vertex is the maximum point.