graph{x^2+12x+36 [-133.2, 26.8, -8.86, 71.14]}
To find the #y#-intercept, substitute #0# in for #x#, which will give you an answer of
#f(x) = 36#
To find the #x#-intercepts, (also known as zeros or roots), substitute #0# in for #f(x)# (which is the #y# value in this case).
Since this is a polynomial with a degree of #2# (which just means that the highest exponent is #2#), you must factor the equation. This will give you an answer of
#f(x) = (x + 6) (x + 6)#
Set each value in the parenthesis equal to #0#, which will give you a result of
#x = -6#
To find the vertex, use the vertex equation
#x = -b/(2a)#
(#a# is the first coefficient, which is #1# in this case, and #b# is the second coefficient, which is #12# in this case).
This will give you an answer of
#x = -6#
To find the #y# value of the vertex, substitute the #-6# in for #x# in the original equation. This will give you
#f(x) = 0#
Therefore, the vertex is #(-6, 0)#. To graph, plot the intercepts and the vertex and connect the points in a parabola. (To find any additional points, choose any number to substitute in for #x# to find the #y# value.)
