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4 years ago

Write f(x)=8x^2-4x+11 in vertex form

Mathematics

1 answer:

Vlad [161]4 years ago

3 0

Answer:

$f(x)=8(x-\frac{1}{4})^{2}+\frac{21}{2}$

$f(x)=8(x-0.25)^{2}+10.5$

Step-by-step explanation:

we have

$f(x)=8x^{2}-4x+11$

This is a vertical parabola open upward (because the leading coefficient is positive)

The vertex is a minimum

Convert to vertex form

Factor the leading coefficient

$f(x)=8(x^{2}-\frac{1}{2}x)+11$

Complete the square. Remember to balance the equation by adding the same constants to each side.

$f(x)=8(x^{2}-\frac{1}{2}x+\frac{1}{16})+11-\frac{1}{2}$

$f(x)=8(x^{2}-\frac{1}{2}x+\frac{1}{16})+\frac{21}{2}$

Rewrite as perfect squares

$f(x)=8(x-\frac{1}{4})^{2}+\frac{21}{2}$ ----> equation in vertex form

$f(x)=8(x-0.25)^{2}+10.5$

The vertex is the point (0.25,10.5)

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"What is the probability that in 10 dice throws, you will throw AT LEAST two ‘3’s on the dice? Assume you’re throwing a single d

dem82 [27]

Answer:

There is a 51.61% probability that in 10 dice throws, you will throw AT LEAST two ‘3’s on the dice.

Step-by-step explanation:

For each throw, there are only two possible outcomes. Either it is a '3', or it is not. This means that we solve this problem using the binomial probability distribution.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinatios of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

In this problem we have that:

There are 6 possible outcomes for the dice. This means that the probability that it is a '3' is $\frac{1}{6} = 0.167$

There are 10 throws, so $n = 10$ .

Probability of throwing AT LEAST two ‘3’s on the dice?

Either you throw less than two, or you throw at least two. The sum of the probabilities of these events is 1. So

$P(X < 2) + P(X \geq 2) = 1$

$P(X \geq 2) = 1 - P(X < 2)$ .

In which

$P(X < 2) = P(X = 0) + P(X = 1)$ .

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{10,0}.(0.167)^{0}.(0.833)^{10} = 0.1609$

$P(X = 1) = C_{10,1}.(0.167)^{1}.(0.833)^{9} = 0.3225$

$P(X < 2) = P(X = 0) + P(X = 1) = 0.1609 + 0.3225 = 0.4834$ .

Finally:

$P(X \geq 2) = 1 - P(X < 2) = 1 - 0.4839 = 0.5161$ .

There is a 51.61% probability that in 10 dice throws, you will throw AT LEAST two ‘3’s on the dice.

5 0

3 years ago

PLEASE HELP QUICK!!!! I WILL GIVE YOU BRAINLIEST!!!

Ksju [112]

The vertex of the function is (-6,-36).

<u>Step-by-step explanation:</u>

f(x) = x²+ 12x

From the above function, we can find the x- coordinate of the vertex as,

x = -b/2a

Here a = 1, b = 12

Plugin the values as,

x = -12 /(2×1) = -6

Now plug in the x value in the above function, we will get y as,

f(x) = y = x² + 12x = (-6)² + 12(-6)

= 36-72 = -36

So the vertex is (-6, -36).

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3 years ago

Find the domain and range of the relation: (-8,8),(-8,7),(-8,6),(-8,5). Then determine whether the relation is a function.

Andrej [43]

The domain is {-8}
The range is {5,6,7,8}
The relation is not a function as the domain value -8 maps to multiple values. All domain values in a relation needs to map to exactly one range value for it be a function.

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4 years ago

What is monomial, binomial, and trinomial?

lozanna [386]

Answer:

monomial—A polynomial with exactly one term.

binomial— A polynomial with exactly two terms.

trinomial—A polynomial with exactly three terms.

Notice the roots: poly– means many.

Step-by-step explanation:

Hope it helps!!

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3 years ago

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What is the value of the expression “three less than the quotient of ten and a number, increased by six” when n = 2?

zloy xaker [14]

So the equation would be 10/N+3-6.
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3 years ago