Answer:
29571 is the answer welcome!!
Step-by-step explanation:
depression, disgust, reduction, demotion, diminishment. elevation(noun) Antonyms: demotion, depression, reduction, diminishment, disgust. elevation(noun)
To find the turning point, or vertex, of this parabola, we need to work out the values of the coefficients b and c.
We are given two different solutions of the equation.
First, (2, 0).
![0=(2)^2+2b+c\\-4=2b+c](https://tex.z-dn.net/?f=0%3D%282%29%5E2%2B2b%2Bc%5C%5C-4%3D2b%2Bc)
Second, (0, 14).
![14=(0)^2+0b+c\\c=14](https://tex.z-dn.net/?f=14%3D%280%29%5E2%2B0b%2Bc%5C%5Cc%3D14)
So we have a value (14) for c. We can substitute that into our first equation to find b.
![-4=2b+c\\-4=2b+14\\-18=2b\\b=-9](https://tex.z-dn.net/?f=-4%3D2b%2Bc%5C%5C-4%3D2b%2B14%5C%5C-18%3D2b%5C%5Cb%3D-9)
We can now plug in our values for b and c into the equation to get its standard form.
![y=x^2-9x+14](https://tex.z-dn.net/?f=y%3Dx%5E2-9x%2B14)
To find the vertex, we can convert this equation to vertex form
![y=a(x-h)^2+k](https://tex.z-dn.net/?f=y%3Da%28x-h%29%5E2%2Bk)
by completing the square.
![y=x^2-9x+14](https://tex.z-dn.net/?f=y%3Dx%5E2-9x%2B14)
![y=x^2-9x+(-4.5)^2+14-(-4.5)^2](https://tex.z-dn.net/?f=y%3Dx%5E2-9x%2B%28-4.5%29%5E2%2B14-%28-4.5%29%5E2)
![y=x^2-9x+20.25+14-20.25](https://tex.z-dn.net/?f=y%3Dx%5E2-9x%2B20.25%2B14-20.25)
![y=(x-4.5)^2-6.25](https://tex.z-dn.net/?f=y%3D%28x-4.5%29%5E2-6.25)
Thus, the vertex is (4.5, –6.25).
We can confirm the solution graphically (see attachment).