Solving Quadratics and Quadratic Formula

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 standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0.

Front

What does it mean to solve a quadratic equation?

Back

To solve a quadratic equation means to find the values of x that make the equation true, which are also known as the roots or zeros of the equation.

Front

What is factoring in the context of quadratic equations?

Back

Factoring is the process of rewriting a quadratic equation as a product of its linear factors, allowing us to find its roots.

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What is the quadratic formula?

Back

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

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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, which determines the nature of the roots.

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What does a positive discriminant indicate?

Back

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 find the vertex of a parabola represented by a quadratic equation?

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