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iren [92.7K]
3 years ago
6

Use the parabola tool to graph the quadratic function f(x)=(x-5)^2+1

Mathematics
1 answer:
andrey2020 [161]3 years ago
5 0

Answer:

Look to the attached graph

Step-by-step explanation:

* Lets revise how to graph the quadratic function

- Find the vertex of it

- Find the y-intercept

- Find the x-intercept

∵ f(x) = (x - 5)² + 1 ⇒ the completing square form

- The completing square form for any quadratic is

 ( x - h)² + k, where h and k are the coordinate of the vertex point

* Lets compare the two forms

∵ (x - h)² + k = (x - 5)² + 1

∴ h = 5 and k = 1

∴ The vertex of the parabola is (5 , 1)

- To find the x-intercept put f(x) = 0

∵ (x - 5)² + 1 = 0 ⇒ subtract 1 from both sides

∴ (x - 5)² = -1 ⇒ the square can not give -ve number

∴ The parabola does not intersect the x-axis

- To find the y-intercept put x = 0

∵ f(0) = (0 - 5)² + 1 = 25 + 1 = 26

∴ The parabola intersects the y-axis at point (0 , 26)

- The parabola is opened upward because the coefficient of x² is +ve

* Now lets graph it

- Look to the attached graph

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substitute the ordered pair (2, 3 )  into the 2 equations

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Hence the ordered pair (2, 3 ) is not a solution to the system of linear equations.

When (2, 3 ) is substituted into the first equation, the equation is true.

When (2, 3 ) is substituted into the second equation, the equation is false.



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Which of the following fractions will convert to terminating decimals?
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B and D

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In a random sample of 200 cars of a particular model,
Aleks04 [339]

By using proportions, We expect 150 defects out of the 10,000 cars if the 3 defects out of the 200 cars sampled is representative of all 10,000 cars.

Option A is correct.

First, let's set up the proportions.

A proportion is an equation in which two ratios are set equal to each other.

We have 3/200 cars with defects and we want to know X for X/10000.

So 3/200 = X/10000

Now solve for X.

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Find out more information about proportions here

brainly.com/question/11609816

#SPJ4

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