### Quadratic Functions

Quadratic functions are those of the form, f(x) = ax^{2 }+ bx + c

Where, a, b and c are all integers

And, f(x) or y is the dependent variable

a is the coefficient of x^{2 }

b is the coefficient of x

c is the y intercept

x is the independent variable

Example

Draw the graph of the quadratic function, f(x) = x^{2 }– 2x -3, for the domain -2 ≤ x ≤ 4.

Solution:

The set of (x, y) values to be plotted and connected in forming the graph representing the quadratic function, parabola (a smooth curve), are found by substituting the values given for x in the domain (-2, -1, 0, 1, 2, 3), in the function, solving for the respective f(x)/ y values.

Given, f(x) = x^{2 }– 2x – 3

Then, f(-2) = (-2)^{2 }– 2(-2) -3 = 4 + 4 – 3 = 5

f(-1) = (-1)^{2 }– 2(-1) – 3 = 1 + 2 -3 = 0

f(0) = (0)^{2 }– 2(0) – 3 = 0 – 0 – 3 = -3

f(1) = (1)^{2 }– 2(1) – 3 = 1 -2 – 3 = -4

f(2) = (2)^{2 }– 2(2) – 3 = 4 – 4 – 3 = -3

f(3) = (3)^{2 }– 2(3) – 3= 9 – 6 – 3 = 0

f(4) = (4)^{2 }– 2(4) – 3 = 16 – 8 – 3 = 5

Therefore the set of (x, y) values are: {(-2, 5), (-1, 0), (0, -3), (1, -4), (2, -3), (3, 0), (4, 5)}

Please watch the video below to see how the graph is drawn.