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 does it mean to factor a quadratic expression?

Back

Factoring a quadratic expression involves rewriting it as a product of two binomials.

Front

What are the roots of a quadratic equation?

Back

The roots of a quadratic equation are the values of x that make the equation equal to zero.

Front

How can you find the roots of a quadratic equation using the quadratic formula?

Back

The roots can be found using the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).

Front

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

Back

The discriminant (b² - 4ac) determines the nature of the roots: if it's positive, there are two distinct 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 in the form (x - p)² = q to easily find the roots.

Front

What are the steps to solve a quadratic equation by factoring?

Back

1. Set the equation to zero. 2. Factor the quadratic expression. 3. Set each factor equal to zero. 4. Solve for x.

Front

What is the vertex form of a quadratic function?

Back

The vertex form of a quadratic function is y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

How do you determine the axis of symmetry for a quadratic function?

Back

The axis of symmetry can be found using the formula x = -b/(2a) from the standard form of the quadratic equation.

Front

What is the relationship between the coefficients of a quadratic equation and its roots?

Back

The sum of the roots is -b/a and the product of the roots is c/a, according to Vieta's formulas.