Quadratic Formula

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What is the Quadratic Formula?

Back

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

Front

What does 'a' represent in the quadratic formula?

Back

'a' represents the coefficient of x² in the quadratic equation ax² + bx + c = 0.

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What does 'b' represent in the quadratic formula?

Back

'b' represents the coefficient of x in the quadratic equation ax² + bx + c = 0.

Front

What does 'c' represent in the quadratic formula?

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'c' represents the constant term in the quadratic equation ax² + bx + c = 0.

Front

What is the discriminant in the quadratic formula?

Back

The discriminant is the part of the quadratic formula under the square root: b² - 4ac. It determines the nature of the roots.

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What does a positive discriminant indicate?

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A positive discriminant indicates that there are two distinct real roots for the quadratic equation.

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What does a zero discriminant indicate?

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A zero discriminant indicates that there is exactly one real root (a repeated root) for the quadratic equation.

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What does a negative discriminant indicate?

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A negative discriminant indicates that there are no real roots, but two complex roots for the quadratic equation.

Front

Solve using the quadratic formula: 8x² + 9x - 329 = 0

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x = -7, x = 47/8.

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What is the vertex form of a quadratic equation?

Back

The vertex form of a quadratic equation is y = a(x - h)² + k, where (h, k) is the vertex of the parabola.