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- anonymous

Can someone help me graph this equation step by step
1.x^2-6x+8=0

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- anonymous

Can someone help me graph this equation step by step
1.x^2-6x+8=0

- schrodinger

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- anonymous

First, do you know what basic shape that function makes?

- anonymous

|dw:1364839464696:dw|

- anonymous

Right. So the vertex is the lowest (or highest) point on the graph. You can find the x-coordinate of the vertex using -b/2a. Do you know what the a, b, and c terms are?

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- anonymous

ok a =1 b=-6 c=8

- anonymous

Right, so -b/2a is what?

- anonymous

the answer would be 3 after doing all the steps

- anonymous

Well, it means that the vertex is at x=3. To find the corresponding "y" of the vertex, plug 3 in for "x" in the function there.

- anonymous

(3,-1)

- anonymous

Okay, so there's your vertex. You know the graph opens up because the quadratic (squared) term is positive. To find where it crosses the x-axis solve the equation for y = 0.
It factors nicely: (x +/- ?)(x +/- ?)

- anonymous

so if x is positive it goes up if x is negative it goes down

- anonymous

No, if x SQUARED is positive it goes up, (x^2)

- anonymous

So how does that function factor. Anything multiply to give 8, but add to give -6?

- anonymous

4 and 2 both are negative

- anonymous

Right, so (x - 4)(x - 2). Set each equal to 0 and solve. The solutions will be the x-values where the parabola crosses the x-axis.

- anonymous

ok I understand now thanks for all your help

- anonymous

Np, you get those and you have your graph.

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