Answer: 0
Step-by-step explanation:
It has no solution
The standard form of a quadratic equation is

, while the vertex form is:

, where (h, k) is the vertex of the parabola.
What we want is to write

as

First, we note that all the three terms have a factor of 3, so we factorize it and write:

.
Second, we notice that

are the terms produced by

, without the 9. So we can write:

, and substituting in

we have:
![\displaystyle{ y=3(x^2-6x-2)=3[(x-3)^2-9-2]=3[(x-3)^2-11]](https://tex.z-dn.net/?f=%5Cdisplaystyle%7B%20y%3D3%28x%5E2-6x-2%29%3D3%5B%28x-3%29%5E2-9-2%5D%3D3%5B%28x-3%29%5E2-11%5D)
.
Finally, distributing 3 over the two terms in the brackets we have:
![y=3[x-3]^2-33](https://tex.z-dn.net/?f=y%3D3%5Bx-3%5D%5E2-33)
.
Answer:
Answer:
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Answer:
m
Step-by-step explanation:
Let
Bas length of box=b
Height of box=h
Material used in constructing of box=36 square m
We have to find the height h and base length b of the box to maximize the volume of box.
Surface area of box=




Volume of box, V=
Substitute the values


Differentiate w. r.t b







The negative value of b is not possible because length cannot be negative.
Again differentiate w.r.t b

At

Hence, the volume of box is maximum at
.




m
Answer:
f(x) = -4x² + 19x - 18
Step-by-step explanation:

i) If it is translated 2 units in the positive x direction, therefore we use f(x-2)

f(x) = 2x² - 9.5x + 6
If it is then translated 3 units in the positive y, we add 3 to the input function to get:

ii) stretched vertically by a factor of 2, we multiply the function by 2 to get:

iii) reflected across the x-axis
we multiply the parent function by –1, to get a reflection about the x-axis.
