Question

Graph each of the equations below on the coordinate grid. Describe each graph and tell whether or not the equation represents a linear function. a. y = 2x + 2b. y = x^2 + 2

Answer 1

a) The fiven function is

$y=2x+2$

This equation represents a linear function, it indicates that for each increase of x, y increases 2 units.

To graph this function you have to determine two points of the line, plot them and cross them with a line.

Since the equation is in slope, intercept form, we can tell directly from it that the y-intercept is (0,2)

For the second point use any value of x and replace it in the formula, for example x=1

$\begin{gathered} y=2\cdot1+2 \\ y=4 \end{gathered}$

For x=1 correspond y=4, that is the second point (1,4)

Next plot the line

b) For the equation

$y=x^2+2$

This equation corresponds to a parabola, i.e. a quadratic function. This is determined because x is squared, this means that, for example for x=-2 and x=2 the function will have the same value of y, except at its vertex.

To draw this function you have to determine its vertex and