Unit 5 Quadratics Review

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What does it mean to translate a graph?

Back

Translating a graph means shifting it horizontally or vertically without changing its shape. For example, translating a graph 4.5 units to the left involves replacing x with (x + 4.5) in the function.

Front

What is the vertex of a quadratic function?

Back

The vertex of a quadratic function is the highest or lowest point on the graph, depending on the direction of the parabola. It can be found using the formula x = -b/(2a) for the function f(x) = ax^2 + bx + c.

Front

How do you reflect a graph over the x-axis?

Back

To reflect a graph over the x-axis, you multiply the entire function by -1. For example, if f(x) = x^2, the reflection would be g(x) = -x^2.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is f(x) = ax^2 + bx + c, 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. It can be found using the formula x = -b/(2a).

Front

What does it mean to stretch a graph horizontally?

Back

Stretching a graph horizontally means to make it wider or narrower. This is done by multiplying the x variable by a factor less than 1 (wider) or greater than 1 (narrower) in the function.

Front

What is the effect of changing the value of 'a' in a quadratic function?

Back

Changing the value of 'a' affects the width and direction of the parabola. If 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards. A larger absolute value of 'a' makes the parabola narrower.

Front

What is the quadratic formula?

Back

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

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. It determines the nature of the roots: if it's positive, there are two real roots; if zero, one real root; if negative, no real roots.