How do you use the important points to sketch the graph of #3x^2-8#?
1 Answer
We have:
# y = 3x^2-8 #
Let us examine some of the properties of this function:
-
This is a polynomial (linear combination of powers of
#x# alone). The highest power of#x# is#2# , so it is a polynomial of degree#2# , or a quadratic function. -
The function is quadratic, so will have a
#uu# shape or an#nn# . The coefficient of#x# is#3# , which is positive, so it will have a#uu# shape. -
If we look at
#f(x)=0# then#3x^2=8 => x^2 = 8/3# leading to two roots,#x=+-sqrt(8/3)# -
If we replace
#x# by#-x# then we have# f(-x) = 3(-x)^2 -8 = 3(x)^2 -8 = f(x) #
So, we deduce that#f(x)# is an even function, and symmetrical about#Oy# -
If we put
#x=0# then we get:# x=0 => f(0) = -8 #
Which gives us enough information to sketch the graph, which here is done using the inbuild Socratic graphing functionality:
graph{3x^2-8 [-5, 5, -10, 5]}
