Flashcard 5 (Factoring and Solving 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 are the roots of a quadratic equation?

Back

The roots of a quadratic equation are the values of x that satisfy the equation, which can be found using factoring, completing the square, or the quadratic formula.

Front

How do you factor a quadratic expression?

Back

To factor a quadratic expression of the form ax² + bx + c, look for two numbers that multiply to ac and add to b, then rewrite the expression as (px + q)(rx + s).

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.

Front

What does it mean to solve a quadratic equation?

Back

To solve a quadratic equation means to find the values of the variable that make the equation true, typically the x-values where the graph intersects the x-axis.

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: if positive, two real roots; if zero, one real root; if negative, no real roots.

Front

What is the process of completing the square?

Back

Completing the square involves rewriting a quadratic equation in the form (x - p)² = q, making it easier to solve for x.

Front

How do you factor a polynomial expression like 5x³ - 7x²?

Back

To factor 5x³ - 7x², first factor out the greatest common factor, which is x², resulting in x²(5x - 7).

Front

What is a perfect square trinomial?

Back

A perfect square trinomial is a quadratic expression that can be factored into the square of a binomial, such as (x + a)² = x² + 2ax + a².

Front

What is the significance of the leading coefficient in a quadratic equation?

Back

The leading coefficient (a) in a quadratic equation ax² + bx + c affects the direction of the parabola: if a > 0, it opens upwards; if a < 0, it opens downwards.