Quadratic Functions and Modeling

Vocabulary

axis of symmetry

line that divides a graph into two halves that are mirror images

nonlinear relationship

relationship between two variables for which a linear model is not a good fit

parabola

shape of the graph of a quadratic function

parent function

function of a certain family type that has the simplest algebraic rule

quadratic function

function, where aa, bb, and cc are real numbers and a0a\neq0, written in the form:
f(x)=ax2+bx+cf(x) = ax^2 + bx + c

quadratic relationship

nonlinear relationship between two variables for which a quadratic function is an appropriate model

regression

mathematical process for determining the equation of the graph that best models a set of data

scatterplot

data display consisting of the graph of a set of ordered pairs

standard form of a quadratic function

quadratic equation, where aa, bb, and cc are real numbers and a0a\neq0, written in the form:
f(x)=ax2+bx+cf(x) = ax^2 + bx + c

vertex

highest or lowest point on a parabola

vertex form of a quadratic function

quadratic equation , where aa, hh, and kk are real numbers and (h,k)(h, k) is the vertex of the parabola, written in the form:
f(x)=a(xh)2+kf(x) = a(x-h)^2+k