2.2 Quadratic FLASHCARD

Front

What is the process of completing the square in a quadratic equation?

Back

Completing the square involves rewriting a quadratic equation in the form (x + p)² = q, allowing for easier solving of the equation.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the solutions of a quadratic equation ax² + bx + c = 0.

Front

How do you identify the 'c' value in a quadratic equation?

Back

The 'c' value is the constant term in the standard form of a quadratic equation ax² + bx + c = 0.

Front

What does it mean to factor a quadratic equation?

Back

Factoring a quadratic equation means expressing it as a product of two binomials, such as (x + p)(x + q) = 0.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of a parabola, depending on its orientation, and can be found using the formula (-b/2a, f(-b/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 positive, there are two real solutions; if zero, one real solution; if negative, no real solutions.

Front

How do you graph a quadratic function?

Back

To graph a quadratic function, identify the vertex, axis of symmetry, and intercepts, then plot points and draw a smooth curve.

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.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the formula x = -b/(2a).

Front

What are the steps to solve a quadratic equation by completing the square?

Back

1. Move the constant to the other side. 2. Divide by 'a' if 'a' is not 1. 3. Add (b/2)² to both sides. 4. Factor the left side and solve for x.