E. Characteristics of the Graphs of Quadratic Functions

One of the easiest ways to make sense of quadratic functions is to analyze them in a real-life context along with their graphs. To build the necessary foundation, we will begin with a look at their graphs and how they compare to those of linear functions.

Let's compare graphs and tables of values for a basic quadratic function and a basic linear function.

Quadratic FunctionLinear Function

second degree function

Eg.

Parabola

first degree function

Eg.

Straight line
x (input)
f(x) (output)
(x,f(x))
−2
(−2, 4)
−1
(−1, 1)
0
(0, 0)
1
(1, 1)
2
(2, 4)
x (input)
g(x) (output)
(x, g(x))
−2
(−2, −2)
−1
(−1, 1)
0
(0, 0)
1
(1, 1)
2
(2, 2)