Quadratic Formula

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What is the Quadratic Formula?

Back

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

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What does 'a' represent in a quadratic equation?

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'a' is the coefficient of x² in the quadratic equation ax² + bx + c = 0. It determines the direction and width of the parabola.

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What does 'b' represent in a quadratic equation?

Back

'b' is the coefficient of x in the quadratic equation ax² + bx + c = 0. It affects the position of the vertex of the parabola.

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What does 'c' represent in a quadratic equation?

Back

'c' is the constant term in the quadratic equation ax² + bx + c = 0. It represents the y-intercept of the parabola.

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How do you identify the vertex of a parabola given by a quadratic equation?

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The vertex (h, k) can be found using h = -b/(2a) and k = f(h), where f(x) is the quadratic function.

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What is the discriminant in the context of 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 the quadratic equation has two distinct real roots.

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What does a zero discriminant indicate?

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

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What does a negative discriminant indicate?

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

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Solve using the Quadratic Formula: 2x² + 17x + 21 = 0

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x = -7, x = -3/2.