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3 years ago

Which graph shows the axis of symmetry for the function f(x) = (x – 2)2 + 1?

Mathematics

2 answers:

viva [34]3 years ago

8 0

Step-by-step explanation:

Please find the attachment of graph representing the axis of symmetry.

We are asked to choose the graph from our given choices, which shows the axis of symmetry for the function:

$f(x)=(x-2)^2+1$

We can see that our function represents a parabola.

Since we know that axis of symmetry is a vertical line that divides parabola into two congruent parts. The axis of symmetry intersects parabola at its vertex.

Let us find the vertex of our given parabola using formula: $x=\frac{-b}{2a}$ , where,

a = Coefficient of $x^{2}.$

b = Coefficient of x.

To apply this formula we will represent our parabola as a quadratic equation $(ax^2+bx+c)$ as:

$f(x)=x^2-4x+4+1$

$f(x)=x^2-4x+5$

Upon substituting a= 1 and b= -4 in the formula we will get,

$x=\frac{-(-4)}{2*1}$

$x=\frac{4}{2}$

$x=2$

Therefore, the vertical line passing through point x = 2 will be the axis of symmetry for our given function and graph B is the correct choice.

svet-max [94.6K]3 years ago

5 0

(x -2)^2 + 1 = 0
x^2 -4x + 5 = 0
The 'x' value of the axis of symmetry = 'x' value of the vertex.
To get this value, take the derivative of x^2 -4x + 5 = 0 which equals
2x -4 =0
x = 2 which equals the axis of symmetry

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Answer:

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Step-by-step explanation:

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2 years ago

The perimeter of the pentagon is 62 units find the length of side BC

kipiarov [429]

recall that the perimeter is simply the sum of all outer sides of a figure.

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3 years ago

Suppose I have an urn with 9 balls: 4 green, 3 yellow and 2 white ones. I draw a ball from the urn repeatedly with replacement.

Mrrafil [7]

Answer:

$E(X_n)=\frac{2(n-1)}{27}$

$E(y)=\frac{14}{9}$

Step-by-step explanation:

From the question we are told that:

Sample size n=9

Number of Green $g=4$

Number of yellow $y=4$

Number of white $w=4$

Probability of Green Followed by yellow P(GY) ball

$P(GY)=\frac{4}{9}*\frac{3}{9}$

$P(GY)=\frac{4}{27}$

Generally the equations for when n is even is mathematically given by

$Probability of success P(S)=\frac{4}{27}$

$Probability of Failure P(F)=\frac{27-4}{27}$

$Probability of Failure P(F)=\frac{23}{27}$

Therefore

$E(X_n)=\frac{n}{2}*P$

$E(X_n)=\frac{n}{2}*\frac{4}{27}$

$E(X_n)=\frac{2n}{27}$

Generally the equations for when n is odd is mathematically given by

$\frac{n-1}{2}$

$E(X_n)=\frac{n-1}{2}*\frac{4}{27}$

$E(X_n)=\frac{2(n-1)}{27}$

Probability of drawing white ball

$P(w)=\frac{2}{9}$

Therefore

$E(w)=\frac{1}{p}$

$E(w)=\frac{1}{\frac{2}{9}}$

$E(w)=\frac{9}{2}$

Therefore

$E(y)=[E(w)-1]\frac{4}{9}$

$E(y)=[\frac{9}{2}-1]\frac{4}{9}$

$E(y)=\frac{14}{9}$

5 0

3 years ago

Which shows 0.00234 written in scientific notation?

topjm [15]

It’s D

the reason why is because the multiplier must be between 1 and 10
(
1
≤
x
≤
10
)
so first more your decimal there which you get:
2.34
then just count how many numbers the decimal jumped, if the decimal moved left the exponent is positive and if it moved right, as in your number, the exponent is negative

yours moved 3

6 0

1 year ago