Factoring quadratics

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What does it mean to factor a quadratic expression?

Back

Factoring a quadratic expression means rewriting it as a product of its linear factors.

Front

What are the steps to factor a quadratic expression of the form ax² + bx + c?

Back

1. Identify a, b, and c. 2. Find two numbers that multiply to ac and add to b. 3. Rewrite the middle term using these numbers. 4. Factor by grouping.

Front

What is the difference of squares formula?

Back

The difference of squares formula states that a² - b² = (a - b)(a + b).

Tags

CCSS.HSA.APR.C.4

Front

How do you factor a perfect square trinomial?

Back

A perfect square trinomial can be factored as (a + b)² or (a - b)², where a² + 2ab + b² = (a + b)² and a² - 2ab + b² = (a - b)².

Tags

CCSS.HSA.APR.C.4

Front

What are the 'zeros' of a quadratic function?

Back

The 'zeros' of a quadratic function are the x-values where the function equals zero, also known as the x-intercepts.

Tags

CCSS.HSF-IF.C.7C

Front

How can you find the zeros of a quadratic equation?

Back

You can find the zeros of a quadratic equation by factoring, using the quadratic formula, or completing the square.

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 significance of the discriminant in a quadratic equation?

Back

The discriminant, given by b² - 4ac, determines the nature of the roots: if positive, there are two distinct real roots; if zero, one real root; if negative, two complex roots.

Tags

CCSS.HSA-REI.B.4B

Front

What is the process of completing the square?

Back

Completing the square involves rewriting a quadratic in the form (x - p)² = q, which helps in solving and graphing the quadratic.

Tags

CCSS.HSA-REI.B.4B