SOLUTION: g(x)=-x^2+7x-6 Find the Vertex and how many x-intercepts. Find the x-intercepts if their are any. How do I do this???

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Question 277995: g(x)=-x^2+7x-6 Find the Vertex and how many x-intercepts. Find the x-intercepts if their are any.
How do I do this???
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
g(x)=-x^2+7x-6 Find the Vertex and how many x-intercepts. Find the x-intercepts if their are any.
write it: y = -x^2 + 7x - 6
:
The x intercept occurs when y = 0
-x^2 + 7x - 6 = 0
:
It's easier to factor if we change the signs, multiply by -1
x^2 - 7x + 6 =
Factors to
(x-6)(x-1) = 0
x = 6, x = 1, the two x intercepts
:
Find the axis of symmetry using the formula x = -b/(2a)
in the original equation: a=-1; b= 7
x = %28-7%29%2F%282%2A-1%29
x = +3.5 is the axis symmetry
:
find the max by substituting 3.5 for x in the original equation
y = -(3.5^2) + 7(3.5) - 6
y = -12.25 + 24.5 - 6
y = 6.25
:
the vertex: x=3.5; y=6.25
:
It looks like this on a graph
+graph%28+300%2C+200%2C+-6%2C+10%2C+-6%2C+8%2C+-x%5E2%2B7x-6%29+
illustrates the two x intercept and the vertex