Quadratic Functions and Modeling

Overview

Description

A quadratic function can be written in the form $f(x) = ax^2 + bx + c$, where $a$, $b$, and $c$ are real numbers and $a\neq0$. The shape of the graph of a quadratic function is a parabola. A vertical line called the axis of symmetry divides a parabola into two halves that are mirror images, with the highest or lowest point of the parabola called the vertex. Quadratic functions can be graphed as transformations of the parent function $f(x) = x^2$ or by using the values of $a$, $b$, and $c$ to identify the vertex and axis of symmetry. If the points in a scatterplot approximate the shape of a parabola, technology can be used to generate a quadratic function that best fits the data.

At A Glance

• The graph of a quadratic function is a parabola.
• Every parabola has a vertex and an axis of symmetry.
• The values of $a$, $b$, and $c$ can be used to determine the vertex and axis of symmetry of $f(x) = ax^2 + bx + c$.
• A quadratic function of the form $f(x) = ax^2 + bx + c$ can be graphed by locating the vertex and the axis of symmetry.
• Quadratic functions can be graphed by transforming the parent function $f(x) = x^2$.
• Data in a scatterplot can show a relationship that is not linear. If the points in a scatterplot approximate the shape of a parabola, a quadratic function may be a better fit for the data.
• Technology can be used to generate a quadratic function that best fits the quadratic relationship between two variables.