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First, do you know what basic shape that function makes?
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?
ok a =1 b=-6 c=8
Right, so -b/2a is what?
the answer would be 3 after doing all the steps
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.
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 +/- ?)
so if x is positive it goes up if x is negative it goes down
No, if x SQUARED is positive it goes up, (x^2)
So how does that function factor. Anything multiply to give 8, but add to give -6?
4 and 2 both are negative
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.
ok I understand now thanks for all your help
Np, you get those and you have your graph.