Quadratic formula

Front

What is the quadratic formula?

Back

The quadratic formula is used to find the solutions of a quadratic equation and is given by: x = (-b ± √(b² - 4ac)) / (2a).

Front

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.

Front

What does 'a' represent in a quadratic equation?

Back

In the quadratic equation ax² + bx + c = 0, 'a' represents the coefficient of x² and determines the parabola's direction (upward if a > 0, downward if a < 0).

Front

What does 'b' represent in a quadratic equation?

Back

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

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What does 'c' represent in a quadratic equation?

Back

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

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What is the discriminant in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root: b² - 4ac. It determines the nature of the roots (real and distinct, real and equal, or complex).

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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 solve a quadratic equation using the quadratic formula?

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To solve a quadratic equation using the quadratic formula, identify a, b, and c, then substitute them into the formula: x = (-b ± √(b² - 4ac)) / (2a).