Solving Quadratic Equations

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of degree 2, typically in the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What is the quadratic formula?

Back

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

Front

What does it mean to factor a quadratic equation?

Back

Factoring a quadratic equation involves expressing it as a product of two binomials, such as (x - p)(x - q) = 0, where p and q are the roots.

Front

How do you complete the square?

Back

To complete the square, rearrange the equation to isolate the constant term, then add and subtract the square of half the coefficient of x.

Front

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.

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root, b² - 4ac, which 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.

Front

How do you solve a quadratic equation by factoring?

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To solve by factoring, rewrite the equation in the form ax² + bx + c = 0, factor it into (x - p)(x - q) = 0, and then set each factor to zero.