Answer:
put all of the expressions into the same form, such as standard form
Step-by-step explanation:
When you're trying to determine whether one expression is equivalent to another, you need to put both of the expressions into the same form. This will generally require some algebraic manipulation using the rules of equality.
Here, you're given a quadratic in standard form. From what we can see of the one partial answer, some of the choices are in vertex form. To determine if they are equivalent, you can do either of two things ...
- Put the given expression into vertex form
- Expand the answer choice to put it in standard form
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<em>For multiple-choice questions</em> of this type, it is often sufficient to look at one or two terms of the different equations. That is usually all it takes to separate a good answer from a bad one.
You can start with the x^2 term. Any answer choice that has an x^2 coefficient different from 1 will be rejected.
Next, you can look at the sign of the x term. Any answer choice that doesn't have a positive x term will be rejected.
Finally, you can look a the constant term. Any answer choice that doesn't have a constant term of +4 will be rejected.
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As it happens, the given equation is a perfect square, so one equivalent is ...
y = (x +2)^2
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When working with quadratics, it can be helpful to memorize a couple of the ways they can be written:
(x +b)^2 = (x^2 +2bx + b^2)
This is a special case of ...
(x +a)(x +b) = x^2 +(a+b)x + ab
![54, a_2, a_3, 128 \\ \\ a_1=54 \\ a_4=128 \\ \\ a_n=a_1 \times r^{n-1} \\ a_4=a_1 \times r^3 \\ 128=54 \times r^3 \\ \frac{128}{54}=r^3 \\ \frac{128 \div 2}{54 \div 2}=r^3 \\ \frac{64}{27}=r^3 \\ \sqrt[3]{\frac{64}{27}}=\sqrt[3]{r^3} \\ \frac{\sqrt[3]{64}}{\sqrt[3]{27}}=r \\ r=\frac{4}{3}](https://tex.z-dn.net/?f=54%2C%20a_2%2C%20a_3%2C%20128%20%5C%5C%20%5C%5C%0Aa_1%3D54%20%5C%5C%0Aa_4%3D128%20%5C%5C%20%5C%5C%0Aa_n%3Da_1%20%5Ctimes%20r%5E%7Bn-1%7D%20%5C%5C%0Aa_4%3Da_1%20%5Ctimes%20r%5E3%20%5C%5C%0A128%3D54%20%5Ctimes%20r%5E3%20%5C%5C%0A%5Cfrac%7B128%7D%7B54%7D%3Dr%5E3%20%5C%5C%20%5Cfrac%7B128%20%5Cdiv%202%7D%7B54%20%5Cdiv%202%7D%3Dr%5E3%20%5C%5C%0A%5Cfrac%7B64%7D%7B27%7D%3Dr%5E3%20%5C%5C%0A%5Csqrt%5B3%5D%7B%5Cfrac%7B64%7D%7B27%7D%7D%3D%5Csqrt%5B3%5D%7Br%5E3%7D%20%5C%5C%0A%5Cfrac%7B%5Csqrt%5B3%5D%7B64%7D%7D%7B%5Csqrt%5B3%5D%7B27%7D%7D%3Dr%20%5C%5C%0Ar%3D%5Cfrac%7B4%7D%7B3%7D)
