the graph of a quadratic equation will look like the top part of an umbrella.
the linear equation can be a constant or it can be a variable with an exponent of 1.
the exponent of 1 is usually not shown because it is implied.
x is the same as x^1, and is usually shown as x, although it can be shown as x^1 when necessary.
some examples of a linear equation.
y = 1
y = x
y = x + 1
the quadratic equation has to have a varible with an exponent of 2, and any other variable in the equation has to be positive and less than 2.
some examples of quadratic equations.
x^2
x^2 + x
x^2 + x + 1
both linear equations and quadratic equatons are polynomials which means that the exponent of any variable in the equation must be a positive integer.
their graphs will be continuous from start to finish.
here's a graph of y = x + 1
here's a graph of y = x^2 + x + 1
here's a graph of y = x^2 + x^-1 + 1
that last graph is not a polynomial because it contains a variable with an exponent that is not a positive integer.
you can see that it is also not continuous because there is a break in the graph at x = 0 where the value of y is undefined because you have a division by 0 when x is equal to 0.
