Graphing Linear and Quadratic Functions

These flashcards cover key concepts related to graphing linear and quadratic equations, as well as the characteristics of their graphs.

Linear Equation

An equation that makes a straight line when graphed, typically in the form of $y = mx + b$.

Graph of $kx + y = 12$

A family of lines showing different slopes based on the value of $k$.

Graph of $x + 2y = 14$

A linear graph that displays a slope of -1/2 when solved for y.

Quadratic Function

A function that can be expressed in the form of $y = ax^2 + bx + c$, resulting in a parabolic graph.

Graph of $y = x^2$

A U-shaped graph that opens upward, with the vertex at the origin (0,0).

Graph of $y = x^2 + 2$

A parabola that opens upward and is shifted up 2 units from the graph of $y = x^2$.

Graph of $y = x^2 - 4$

A parabola that opens upward and is shifted down 4 units from the graph of $y = x^2$.

Parameter $c$ in $y = x^2 + c$

Determines the vertical shift of the parabola: if $c > 0$, it shifts up; if $c < 0$, it shifts down.

Table of Values

A set of pairs of x and y values that help plot the graphs accurately based on the equation.