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Question 60702: I need to graph each function
y=x2-5x+6 (I tried to subscript the 2 but it didnt work)
f(x)=x2+4 (I tried to subscript the 2 but it didnt work)
Answer by funmath(2933)   (Show Source):
You can put this solution on YOUR website! Graph each function
y=x^2-5x+6 <--you can use ^ to raise something to a power.
This is a parabola.
Because x^2 is positive, we know it opens up.
The y-intercept can be found by letting x=0
y=0^2-5(0)+6
y=0+0+6
y=6 Plot (0,6)
:
To find the x-intercept, let y=0
0=x^2-5x+6
0=(x-3)(x-2)
x-3=0 and x-2=0
x=3 and x=2
Plot (3,0) and (2,0)
The axis of symmetry and x coordinate of the vertex can be found using the formula 
a=1, b=-5, and c=6
x=2.5
y=6.25-12.5+6
y=-.25 Plot (2.5,-.25)
You now know that it looks like this.
:
f(x)=x^2+4
x^2 is positive, so it opens up.
The y-intercept is:
f(0)=0^2+4
f(0)=4 Plot (0,4)
:
There is no x-intercept because 0=x^2+4 has no real solution.
:
The vertex is the y intercept because there's no b. Because you only know one point. Plot some points on the left and right side of x=0.
f(1)=1^2+4
f(1)=1+4
f(1)=5 Plot (1,5)
f(-1)=(-1)^2+4
f(-1)=1+4
f(-1)=5 Plot(-1,5)
I'll let you find and plot f(-2) and f(2).
Connect your points and you have:
Happy Calculating!!!
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