Question 462469: Using the formula f(x) = x^2 – 2x + 1, find if it has a maximum or minimum and give that point. Also give x-intercepts.
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! Using the formula f(x) = x^2 – 2x + 1, find if it has a maximum or minimum and give that point. Also give x-intercepts.
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f(x) = x^2 – 2x + 1
Examining the coefficient associated with the x^2 term, we see that it is "positive" -- this means the vertex is a MINIMUM.
x = -b/(2a)
x = -(-2)/(2*1)
x = (2)/(2)
x = 1
To find the 'y', plug above value back into:
f(x) = x^2 – 2x + 1
f(1) = 1^2 – 2(1) + 1
f(1) = 1 – 2 + 1
f(1) = 0
Vertex: (1,0)
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x-intercepts: set f(x) to zero and solve for x:
f(x) = x^2 – 2x + 1
0 = x^2 – 2x + 1
0 = (x-1)(x-1)
x = 1
x-intercept at (1,0) (same as the vertex, in this case)
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