<span>Differentiating :
y' = 1 + sec^2(x),
</span><span>
cosπ=−1</span><span>
plug in pi = -1 ,for x:
1 + sec^2(pi) = 1 + (-1)^2
= 2</span>
Step-by-step explanation:
the answer is 6.125 and its will be divided by 125
Answer:
(5,-6)
Step-by-step explanation:
ONE WAY:
If
, then
.
Let's simplify that.
Distribute with
:
![f(x-2)=(x-2)^2-6x+12+3](https://tex.z-dn.net/?f=f%28x-2%29%3D%28x-2%29%5E2-6x%2B12%2B3)
Combine the end like terms
:
![f(x-2)=(x-2)^2-6x+15](https://tex.z-dn.net/?f=f%28x-2%29%3D%28x-2%29%5E2-6x%2B15)
Use
identity for
:
![f(x-2)=x^2-4x+4-6x+15](https://tex.z-dn.net/?f=f%28x-2%29%3Dx%5E2-4x%2B4-6x%2B15)
Combine like terms
and
:
![f(x-2)=x^2-10x+19](https://tex.z-dn.net/?f=f%28x-2%29%3Dx%5E2-10x%2B19)
We are given
.
So we have that
.
The vertex happens at
.
Compare
to
to determine
.
![a=1](https://tex.z-dn.net/?f=a%3D1)
![b=-10](https://tex.z-dn.net/?f=b%3D-10)
![c=19](https://tex.z-dn.net/?f=c%3D19)
Let's plug it in.
![\frac{-b}{2a}](https://tex.z-dn.net/?f=%5Cfrac%7B-b%7D%7B2a%7D)
![\frac{-(-10)}{2(1)}](https://tex.z-dn.net/?f=%5Cfrac%7B-%28-10%29%7D%7B2%281%29%7D)
![\frac{10}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B10%7D%7B2%7D)
![5](https://tex.z-dn.net/?f=5)
So the
coordinate is 5.
Let's find the corresponding
coordinate by evaluating our expression named
at
:
![5^2-10(5)+19](https://tex.z-dn.net/?f=5%5E2-10%285%29%2B19)
![25-50+19](https://tex.z-dn.net/?f=25-50%2B19)
![-25+19](https://tex.z-dn.net/?f=-25%2B19)
![-6](https://tex.z-dn.net/?f=-6)
So the ordered pair of the vertex is (5,-6).
ANOTHER WAY:
The vertex form of a quadratic is
where the vertex is
.
Let's put
into this form.
We are given
.
We will need to complete the square.
I like to use the identity
.
So If you add something in, you will have to take it out (and vice versa).
![x^2-6x+3](https://tex.z-dn.net/?f=x%5E2-6x%2B3)
![x^2-6x+(\frac{6}{2})^2+3-(\frac{6}{2})^2](https://tex.z-dn.net/?f=x%5E2-6x%2B%28%5Cfrac%7B6%7D%7B2%7D%29%5E2%2B3-%28%5Cfrac%7B6%7D%7B2%7D%29%5E2)
![(x+\frac{-6}{2})^2+3-3^2](https://tex.z-dn.net/?f=%28x%2B%5Cfrac%7B-6%7D%7B2%7D%29%5E2%2B3-3%5E2)
![(x+-3)^2+3-9](https://tex.z-dn.net/?f=%28x%2B-3%29%5E2%2B3-9)
![(x-3)^2+-6](https://tex.z-dn.net/?f=%28x-3%29%5E2%2B-6)
So we have in vertex form
is:
.
The vertex is (3,-6).
So if we are dealing with the function
.
This means we are going to move the vertex of
right 2 units to figure out the vertex of
which puts us at (3+2,-6)=(5,-6).
The
coordinate was not effected here because we were only moving horizontally not up/down.