Square Equations

Front

What is a square equation?

Back

A square 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 complete the square?

Back

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

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0.

Front

How do you find the vertex of a parabola given by a quadratic equation?

Back

The vertex can be found using the formula (-b/2a, f(-b/2a)), where f(x) is the quadratic function.

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 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.

Front

What does a zero discriminant indicate?

Back

A zero discriminant indicates that the quadratic equation has exactly one real root (a repeated root).

Front

What does a negative discriminant indicate?

Back

A negative discriminant indicates that the quadratic equation has no real roots, but two complex roots.

Front

How do you complete the square for the equation x² - 6x + 5 = 0?

Back

1. Move the constant: x² - 6x = -5. 2. Take half of -6, square it (9), and add to both sides: x² - 6x + 9 = 4. 3. Factor: (x - 3)² = 4.