It would be answer A since moving it right from the axis makes the x part include a negative next to the number that's being shifted from the axis, and when reflecting it across the x-axis, the number outside of the parenthesis becomes negative
I think the correct answer from the choices listed above is option D. The function that will produce the same graph as the function y=(x+1)(x-3) would be <span>y=x^2-2x-3. Both equations are the same. You can confirm it by simplifying the equation. Hope this answers the question.</span>
When we are to divide the line segment such that the ratio is 1:2, there are actually 3 parts of the segment. First, we determine the distance between the coordinates and divide the distance by 3. Then, we add the quotient to the x-coordinate.
x-coordinate: (2 - 9) / 3 = -7/3
y-coordinate: (6 - 3 ) / 3 = 1
Adding them to the coordinates of a,
x - coordinate: (9 - 7/3) = 20/3
y - coordinate: (3 + 1) = 4
Thus, the coordinates are (20/3, 4).
Answer:
The solutions are
and ![x=\frac{1-\sqrt{7}}{2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B1-%5Csqrt%7B7%7D%7D%7B2%7D)
Step-by-step explanation:
we have
![0=-2x^{2}+2x+3](https://tex.z-dn.net/?f=0%3D-2x%5E%7B2%7D%2B2x%2B3)
Group terms that contain the same variable, and move the constant to the opposite side of the equation
![-3=-2x^{2}+2x](https://tex.z-dn.net/?f=-3%3D-2x%5E%7B2%7D%2B2x)
Factor the leading coefficient
![-3=-2(x^{2}-x)](https://tex.z-dn.net/?f=-3%3D-2%28x%5E%7B2%7D-x%29)
Complete the square. Remember to balance the equation by adding the same constants to each side.
![-3-0.5=-2(x^{2}-x+0.5^{2})](https://tex.z-dn.net/?f=-3-0.5%3D-2%28x%5E%7B2%7D-x%2B0.5%5E%7B2%7D%29)
![-3.5=-2(x^{2}-x+0.5^{2})](https://tex.z-dn.net/?f=-3.5%3D-2%28x%5E%7B2%7D-x%2B0.5%5E%7B2%7D%29)
Rewrite as perfect squares
![-3.5=-2(x-0.5)^{2}](https://tex.z-dn.net/?f=-3.5%3D-2%28x-0.5%29%5E%7B2%7D)
![7/4=(x-0.5)^{2}](https://tex.z-dn.net/?f=7%2F4%3D%28x-0.5%29%5E%7B2%7D)
square root both sides
![x-0.5=(+/-)\sqrt{\frac{7}{4}}](https://tex.z-dn.net/?f=x-0.5%3D%28%2B%2F-%29%5Csqrt%7B%5Cfrac%7B7%7D%7B4%7D%7D)
![x-\frac{1}{2}=(+/-)\frac{\sqrt{7}}{2}](https://tex.z-dn.net/?f=x-%5Cfrac%7B1%7D%7B2%7D%3D%28%2B%2F-%29%5Cfrac%7B%5Csqrt%7B7%7D%7D%7B2%7D)
![x=\frac{1}{2}(+/-)\frac{\sqrt{7}}{2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B1%7D%7B2%7D%28%2B%2F-%29%5Cfrac%7B%5Csqrt%7B7%7D%7D%7B2%7D)
![x=\frac{1+\sqrt{7}}{2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B1%2B%5Csqrt%7B7%7D%7D%7B2%7D)
![x=\frac{1-\sqrt{7}}{2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B1-%5Csqrt%7B7%7D%7D%7B2%7D)
It should be eight if I remember correctly