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Circle the problems that are in standard form. If it is not in standard form,re-write in standard form.

Circle the problems that are in standard form. If it is not in standard form,re-write-example-1

2 Answers

5 votes

Final answer:

To determine if a problem is in standard form, look at its equation. Rearrange the equation to match the standard form.

Step-by-step explanation:

In order to determine if a problem is in standard form, we need to look at its equation. The standard form of a circle equation is (x - h)^2 + (y - k)^2 = r^2.

Let's say we have an equation of a circle, such as x^2 + y^2 + 4x - 6y - 3 = 0.

To determine if this equation is in standard form, we need to rearrange it to match the standard form. We can start by grouping the x terms together and the y terms together, which gives us (x^2 + 4x) + (y^2 - 6y) = 3.

Next, we complete the square for both x and y. For x, we add (4/2)^2 = 4 to both sides of the equation, giving us (x^2 + 4x + 4) + (y^2 - 6y) = 7.

For y, we add (-6/2)^2 = 9 to both sides of the equation, giving us (x^2 + 4x + 4) + (y^2 - 6y + 9) = 7 + 4 + 9 = 20.

Finally, we can write the equation in standard form as (x + 2)^2 + (y - 3)^2 = 20.

User Dan Rosenstark
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Explanation

The equation can be expressed in standard form.


f(x)=a_1x^n+a_2x^(n-1)+a_3x^(n-2)+a_4x^(n-3)+........+a_0

Part A:


x^3-11x^2

Answer: This already in a standard form

Part B


2+3x+4x^2+3x^3

We can then rearrange to have;

Answer:


3x^3+4x^2+3x+2

Part C


-3x+17x^4+2x^2

We can then rearrange to have;

Answer:


17x^4+2x^2-3x

Part D


-1+3x+2x^2

We can then rearrange to have;

Answer:


2x^2+3x-1

User Yossi Sternlicht
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