You can
put this solution on YOUR website!graph f(x)=|x-3|+2 include all intercepts and the vertex.
:
To find the y intercept, let x=0 and solve for y:
f(x)=y=|x-3|+2
y=|0-3|+2
y=|-3|+2
y=3+2
y=5 Plot (0,5) the y-intercept.
:
To find the x-intercept, let y=0 and solve for x:
0=|x-3|+2
-2=|x-3|+2-2
-2=|x-3| An absolute value is always positive, therefore there are no x-intercepts.
:
To find the vertex:
(x-3)+2=-(x-3)+2
x-3+2=-x+3+2
x-1=-x+5
x-1+1=-x+5+1
x=-x+6
x+x=x-x+6
2x=6
2x/2=6/2
x=3 This is the x coordinate of the vertex.
y=|3-3|+2
y=|0|+2
y=2
The vertex is (3,2) Plot that.
Since there were no x-intercepts, you may want to let x= a couple of other numbers to get a couple of more points.
Happy Calculating!!!
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