Unit 4A Quadratics Review

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. It can be found using the formula x = -b/(2a) for a quadratic in the form ax^2 + bx + c.

Front

What are the three forms of quadratic equations?

Back

1. Standard Form: ax^2 + bx + c = 0 2. Factored/Intercept Form: a(x - p)(x - q) = 0 3. Vertex Form: a(x - h)^2 + k = 0, where (h, k) is the vertex.

Front

How do you find the area of a rectangle?

Back

Area = length × width.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation. It can be found using the formula (h, k) in the vertex form of a quadratic equation.

Front

What is the quadratic formula?

Back

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

Front

How do you solve a quadratic equation by factoring?

Back

To solve by factoring, rewrite the equation in the form ax^2 + bx + c = 0, factor it into (x - p)(x - q) = 0, and then set each factor to zero: x - p = 0 and x - q = 0.

Front

What are consecutive integers?

Back

Consecutive integers are numbers that follow each other in order, such as 1, 2, 3 or 14, 15.

Front

What does it mean for a quadratic function to have real roots?

Back

A quadratic function has real roots if the discriminant (b² - 4ac) is greater than or equal to zero.

Front

How do you determine the width of a rectangle if the area and length are known?

Back

Width = Area / Length.

Front

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

Back

The discriminant 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.