Question 489817: Consider the function f(x) = 3x^2 - 30x - 1
a. determine without graphing, does the function have a minimum or maximum value?
b. Find the minimum or maximum value and determine where it occurs.
c. Identify the functions domain and range
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Consider the function f(x) = 3x^2 - 30x - 1
a. determine without graphing, does the function have a minimum or maximum value?
b. Find the minimum or maximum value and determine where it occurs.
c. Identify the functions domain and range
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y=3x^2-30x-1
a. Because the lead coefficient is >0, this parabola opens upwards which means function has a minimum.
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b.completing the square
y=3(x^2-10x+25)-1-75
y=3(x-5)^2-76
This is an equation of a parabola of the standard form: y=A(x-h)^2+k, with (h,k) being the (x,y) coordinates of the vertex.
coordinates of the vertex:(5,-76)
minimum value=-76 at x=5
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c. Domain (-∞,∞), Range [-76,∞)
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