12.9.24 A2 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 the Quadratic Formula?

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

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What does 'b' represent in the Quadratic Formula?

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

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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.

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What is the discriminant in the context of the Quadratic Formula?

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

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What does a positive discriminant indicate?

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A positive discriminant (b² - 4ac > 0) 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 (b² - 4ac = 0) 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 (b² - 4ac < 0) indicates that the quadratic equation has no real roots, but two complex roots.

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How do you apply the Quadratic Formula to the equation 2x² + 4x - 6 = 0?

Back

Identify a = 2, b = 4, c = -6. Then, use the formula: x = (-4 ± √(4² - 4*2*(-6))) / (2*2).

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What is the first step in using the Quadratic Formula?

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The first step is to identify the coefficients a, b, and c from the quadratic equation in standard form.