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sp2606 [1]
3 years ago
6

Write the function in vertex form. y=4x2 - 8x + 5

Mathematics
2 answers:
Tema [17]3 years ago
8 0

a=4, b=-8, c=5

h=-b/2a= -(-8)/2(4)

8/8=h=1

K= a(h)^2+b(h)+c

K= 4(1)^2-8(1)+5

K= 4-8+5

K= 1, Vertex  Form: a(x-h)^2+k

Vertex Form: Y= 4(X-(1)^2+K

Y= 4(x-1)^2+1

Firdavs [7]3 years ago
6 0
You will have to complete the square
factor the 4 out of the first two terms
y = 4(x^2 - 2x) + 5

x^2 - 2x + 1 = (x - 1)^2
we want what we have to look like this
the difference between (x^2 - 2x) and (x^2 - 2x + 1) is the +1
so we add a 1 and subtract a 1 to keep balance

y = 4(x^2 - 2x + 1  -1) + 5
y = 4(x^2 - 2x + 1) - 4 + 5   [moved the extra -1 out of it and distributive property]
y = 4(x - 1)^2 + 1   [factored and added like terms]

y = 4(x-1)^2 + 1
or
y - 1 = 4(x-1)^2

is now in vertex form.
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Okay so lets look at this.

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The quarterly returns for a group of 51 mutual funds are well modeled by a Normal model with a mean of 7.4​% and a standard devi
Wittaler [7]

Answer:

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Step-by-step explanation:

68% of data will fall within 1 standard deviation of the mean; 95% of data will fall within 2 standard deviations of the mean; and 99.7% of data will fall within 3 standard deviations of the mean.

Breaking this down, we find that 34% of data fall from the mean to 1 standard deviation above the mean; 13.5% of data fall from 1 standard deviation above the mean to 2 standard deviations above the mean; 2.35% of data fall from 2 standard deviations above the mean to 3 standard deviations above the mean; and 0.15% of data fall above 3 standard deviations above the mean.

The same percentages apply to the standard deviations below the mean.

The highest 50% of data will fall from the mean to the end of the right tail.  This means the inequality for the highest 50% will be x ≥ 0.074, the mean.

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8 0
4 years ago
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Answer:

A

Step-by-step explanation:

We are given the function:

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And we want to find:

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So, we need to determine whether or not the limit exists. In other words, we will find the two one-sided limits.

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Since we are approaching from the left, we will use the first equation:

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By direct substitution:

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Since we are approaching from the right, we will use the second equation:

=\displaystyle \lim_{x\to -1^+}\frac{2}{\cos(\pi x)}

Direct substitution:

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So, we can see that:

\displaystyle \displaystyle \lim_{x\to-1^-}f(x)=\displaystyle \lim_{x\to -1^+}f(x) =-2

Since both the left- and right-hand limits exist and equal the same thing, we can conclude that:

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