Solving Quadratic Equations

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 does it mean to solve a quadratic equation by taking the square root?

Back

To solve a quadratic equation by taking the square root, isolate the x² term and then take the square root of both sides, resulting in two possible solutions: ±√(value).

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 complete the square for x² + 12x?

Back

Add (12/2)² = 36 to both sides, resulting in x² + 12x + 36 = (x + 6)².

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.

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, found using factoring, completing the square, or the quadratic formula.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of any quadratic equation.

Front

How do you factor the quadratic equation x² + 7x + 12?

Back

The equation factors to (x + 3)(x + 4) = 0, giving roots x = -3 and x = -4.

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.

Front

What does a positive discriminant indicate?

Back

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