Solving Quadratic Equations - Factoring

Front

What is a quadratic equation?

Back

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

Front

What are the methods to solve quadratic equations?

Back

The methods to solve quadratic equations include factoring, completing the square, using the quadratic formula, and graphing.

Tags

CCSS.HSA-REI.B.4B

Front

What is factoring in the context of quadratic equations?

Back

Factoring is the process of expressing a quadratic equation as a product of its linear factors.

Tags

CCSS.HSA-REI.B.4B

Front

How do you factor a quadratic equation of the form x² + bx + c?

Back

To factor a quadratic equation of the form x² + bx + c, find two numbers that multiply to c and add to b, then express it as (x + m)(x + n) where m and n are the two numbers.

Front

What is the zero-product property?

Back

The zero-product property states that if the product of two factors is zero, then at least one of the factors must be zero.

Tags

CCSS.HSA-REI.B.4B

Front

How do you apply the zero-product property to solve quadratic equations?

Back

To apply the zero-product property, set each factor of the factored quadratic equation equal to zero and solve for the variable.

Tags

CCSS.HSA-REI.B.4B

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (D = b² - 4ac) determines the nature of the roots of a quadratic equation: if D > 0, there are two distinct real roots; if D = 0, there is one real root; if D < 0, there are no real roots.

Tags

CCSS.HSA-REI.B.4B

Front

What does it mean for a quadratic equation to have complex roots?

Back

A quadratic equation has complex roots when the discriminant is negative, resulting in roots that are not real numbers and can be expressed in the form a + bi.

Tags

CCSS.HSN.CN.C.9

Front

How can you solve a quadratic equation by completing the square?

Back

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

Tags

CCSS.HSA-REI.B.4B

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.