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, i.e., the roots of the equation.

Tags

CCSS.HSA-REI.B.4B

Front

What is factoring in the context of quadratic equations?

Back

Factoring is the process of rewriting a quadratic equation as a product of two binomials, which can then be set to zero to find the 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?

Back

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?

Back

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

Tags

CCSS.HSA-REI.B.4B

Front

What does a zero discriminant indicate?

Back

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 solve a quadratic equation by completing the square?

Back

To solve by completing the square, rearrange the equation to isolate the constant, then add the square of half the coefficient of x to both sides, and solve for x.

Tags

CCSS.HSA-REI.B.4B