Unit 8 - 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 is the standard form of a quadratic equation?

Back

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

Front

What does the 'a' in a quadratic equation represent?

Back

In the quadratic equation ax² + bx + c = 0, 'a' represents the coefficient of x² and determines the direction of the parabola (upward if a > 0, downward if a < 0).

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 expression b² - 4ac in the quadratic formula, which determines the nature of the roots: if positive, two real roots; if zero, one real root; if negative, no real roots.

Front

How do you convert a quadratic equation to standard form?

Back

To convert a quadratic equation to standard form, rearrange it to the form ax² + bx + c = 0 by moving all terms to one side.

Front

What is factoring in the context of quadratic equations?

Back

Factoring is the process of rewriting a quadratic equation as a product of two binomials, which can help in finding the roots.

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on whether it opens upward or downward.

Front

How do you find the vertex of a quadratic function?

Back

The vertex (h, k) of a quadratic function in standard form y = ax² + bx + c can be found using h = -b/(2a) and k = f(h).

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 equation x = -b/(2a).