Question 277995
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 
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The x intercept occurs when y = 0
-x^2 + 7x - 6 = 0
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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 = {{{(-7)/(2*-1)}}}
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
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the vertex: x=3.5; y=6.25
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It looks like this on a graph
{{{ graph( 300, 200, -6, 10, -6, 8, -x^2+7x-6) }}}
illustrates the two x intercept and the vertex