Solving Quadratics and Quadratic Formula

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What is a quadratic equation?

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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.

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What is the standard form of a quadratic equation?

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

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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.

Tags

CCSS.HSA-REI.B.4B

Front

What is factoring in the context of quadratic equations?

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

Tags

CCSS.HSA-REI.B.4B

Front

What is the quadratic formula?

Back

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

Tags

CCSS.HSA-REI.B.4B

Front

What is the discriminant in a quadratic equation?

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

Tags

CCSS.HSA-REI.B.4B

Front

What does a positive discriminant indicate?

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A positive discriminant indicates that the quadratic equation has two distinct real roots.

Tags

CCSS.HSA-REI.B.4B

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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).

Tags

CCSS.HSA-REI.B.4B

Front

What does a negative discriminant indicate?

Back

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

Tags

CCSS.HSA-REI.B.4B

Front

How do you find the vertex of a parabola represented by a quadratic equation?

Back

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