Question 965749
the graph of a linear eqution will be a straight line.


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


{{{graph(400,400,-10,10,-10,10,x+1)}}}


here's a graph of y = x^2 + x + 1


{{{graph(400,400,-10,10,-10,10,x^2+x+1)}}}


here's a graph of y = x^2 + x^-1 + 1


{{{graph(400,400,-10,10,-10,10,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.


x^-1 is the same a 1/x.


when x is equal to 0, that becomes 1/0.


the first 2 graphs are polynopmials.


the last graph is not.