Answer:
![\large\boxed{y=2(x+1)^2-3}](https://tex.z-dn.net/?f=%5Clarge%5Cboxed%7By%3D2%28x%2B1%29%5E2-3%7D)
Step-by-step explanation:
The vertex form of an equation of a parabola:
![y=a(x-h)^2+k](https://tex.z-dn.net/?f=y%3Da%28x-h%29%5E2%2Bk)
(h, k) - vertex
We have
![y=2x^2+4x-1=2\left(x^2+2x-\dfrac{1}{2}\right)](https://tex.z-dn.net/?f=y%3D2x%5E2%2B4x-1%3D2%5Cleft%28x%5E2%2B2x-%5Cdfrac%7B1%7D%7B2%7D%5Cright%29)
We must use the formula: ![(a+b)^2=a^2+2ab+b^2\qquad(*)](https://tex.z-dn.net/?f=%28a%2Bb%29%5E2%3Da%5E2%2B2ab%2Bb%5E2%5Cqquad%28%2A%29)
![2\left(x^2+2(x)(1)-\dfrac{1}{2}\right)=2\bigg(\underbrace{x^2+2(x)(1)+1^2}_{(*)}-1^2-\dfrac{1}{2}\bigg)\\\\=2\left((x+1)^2-1-\dfrac{1}{2}\right)=2\left((x+1)^2-\dfrac{3}{2}\right)](https://tex.z-dn.net/?f=2%5Cleft%28x%5E2%2B2%28x%29%281%29-%5Cdfrac%7B1%7D%7B2%7D%5Cright%29%3D2%5Cbigg%28%5Cunderbrace%7Bx%5E2%2B2%28x%29%281%29%2B1%5E2%7D_%7B%28%2A%29%7D-1%5E2-%5Cdfrac%7B1%7D%7B2%7D%5Cbigg%29%5C%5C%5C%5C%3D2%5Cleft%28%28x%2B1%29%5E2-1-%5Cdfrac%7B1%7D%7B2%7D%5Cright%29%3D2%5Cleft%28%28x%2B1%29%5E2-%5Cdfrac%7B3%7D%7B2%7D%5Cright%29)
Use the distributive formula a(b + c) = ab + ac
![2(x+1)^2+2\left(-\dfrac{3}{2}\right)=2(x+1)^2-3](https://tex.z-dn.net/?f=2%28x%2B1%29%5E2%2B2%5Cleft%28-%5Cdfrac%7B3%7D%7B2%7D%5Cright%29%3D2%28x%2B1%29%5E2-3)
Answer: Second option
Explanation: As u can see the fraction is being multiplied 3 times.
1.
a.Irrational
b. Irrational
c. Rational
d.Irrational
2.
Is Rational
Is an integer
Is a whole number
3.
Is Rational
Is a real number
4.
Is Rational
========================
As far as I can tell you got them all correct, well done :D
Answer:
No. Hardy should have multiplied by the scale factor to find the missing length.
Step-by-step explanation:
The answer is 5x-11
You have to distrivute 1/3 into 6x and -9 and after you have your answer for those you can combine like terms.