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suter [353]
3 years ago
14

In the function f(x)=(x-2)^2+4, the minimum value occurs when x is

Mathematics
2 answers:
Vinil7 [7]3 years ago
6 0

The graph of the function is a parabola. 

The nose comes down as far as y=4 but no farther.

That happens when  (x - 2)² = 0 , and THAT happens when x = 2 .

madreJ [45]3 years ago
6 0
F(x) = (x - 2)² + 4
f(x) = (x - 2)(x - 2) + 4
f(x) = (x(x - 2) - 2(x - 2)) + 4
f(x) = (x(x) - x(2) - 2(x) + 2(2)) + 4
f(x) = (x² - 2x - 2x + 4) + 4
f(x) = (x² - 4x + 4) + 4
f(x) = x² - 4x + 4 + 4
f(x) = x² - 4x + 8

x = -\frac{b}{2a} = -\frac{-4}{2(1)} = -\frac{-4}{2} = -(-2) = 2
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In 10 seconds, the garden hose will emit 15 quarts of water.  

Step-by-step explanation:

The amount of water emitted by the garden hose over time can be expressed as a ratio:  9/6, or 9 quarts of water for every 6 seconds of time.  We can then simplify this ratio to 3/2, or 3 quarts of water for every 2 seconds of time.  Since the ratio will remain constant, or the same, over time, we can set up an equivalent ratio, or fraction to find the amount of water emitted in 10 seconds:  3/2 = x/10.  We look at the denominators and see that 2 x 5 = 10.  In order to make the ratios equivalent, we would also multiply the numerator by 5:  3 x 5 = 15, which gives us the amount of water emitted in 10 seconds.  

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Answer:

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Step-by-step explanation:

To find the inverse of a function f (x) follow the steps below:

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3) Exchange the variable x with the variable y

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