Answer:
1. Add 5 to both sides
2.Divide both sides by 4
3. Flip the inequality sign( this is because when ever you divide/multiply by a negative number you have to flip the inequality sign)
4. Rewrite so that p is on the left side
ANSWER
The vertex of the graph of
![y = \frac{1}{3} {(x - 9)}^{2} + 5](https://tex.z-dn.net/?f=y%20%3D%20%20%5Cfrac%7B1%7D%7B3%7D%20%20%7B%28x%20-%209%29%7D%5E%7B2%7D%20%20%2B%205)
is
![(9,5)](https://tex.z-dn.net/?f=%289%2C5%29)
EXPLANATION
The vertex form of a parabola is given by
![y = a {(x - h)}^{2} + k](https://tex.z-dn.net/?f=y%20%3D%20a%20%7B%28x%20-%20h%29%7D%5E%7B2%7D%20%20%2B%20k)
where
![V(h,k)](https://tex.z-dn.net/?f=V%28h%2Ck%29)
is the vertex of the parabola.
The function given to us is
![y = \frac{1}{3} {(x - 9)}^{2} + 5](https://tex.z-dn.net/?f=y%20%3D%20%20%5Cfrac%7B1%7D%7B3%7D%20%20%7B%28x%20-%209%29%7D%5E%7B2%7D%20%20%2B%205%20)
This is already in the vertex form.
When we compare this to the general vertex form, we have,
![a = \frac{1}{3}](https://tex.z-dn.net/?f=a%20%3D%20%20%5Cfrac%7B1%7D%7B3%7D%20)
![h = 9](https://tex.z-dn.net/?f=h%20%3D%209)
and
![k = 5](https://tex.z-dn.net/?f=k%20%3D%205)
Therefore the vertex of the parabola is
![V(9,5)](https://tex.z-dn.net/?f=V%289%2C5%29)
Hence the correct answer is option A.
Answer:
44%
Step-by-step explanation:
100 + 20 = 120/100
(1.2)^2=1.44
144 - 100 = 44%
Answer:
f(x) is shifted to the left 2 units of g(x)
f(x) will not be shifted vertically since we did not add anything to g(x)
Step-by-step explanation:
g(x) = x^2+2
f(x) = g(x+2)
When we shift with h(x+c) it is a horizontal shift
if c>0 it moves it left c units
if c< 0 it moves it right c units
Since c is 2, this is shifted left 2 units
f(x) is shifted to the left 2 units of g(x)
When we shift with h(x)+c it is a vertical shift
if c>0 it moves it up c units
if c< 0 it moves it down c units
f(x) will not be shifted vertically since we did not add anything to g(x)
![g(p) \cdot h(p) = p^{4}+2 p^{3}-8 p^{2}-2p+4](https://tex.z-dn.net/?f=g%28p%29%20%5Ccdot%20h%28p%29%20%3D%20p%5E%7B4%7D%2B2%20p%5E%7B3%7D-8%20p%5E%7B2%7D-2p%2B4)
Solution:
Given data:
and ![h(p)=\left(p^{3}+4 p^{2}-2\right)](https://tex.z-dn.net/?f=h%28p%29%3D%5Cleft%28p%5E%7B3%7D%2B4%20p%5E%7B2%7D-2%5Cright%29)
To find
:
![g(p) \cdot h(p)= (p-2)\cdot \left(p^{3}+4 p^{2}-2\right)](https://tex.z-dn.net/?f=g%28p%29%20%5Ccdot%20h%28p%29%3D%20%28p-2%29%5Ccdot%20%5Cleft%28p%5E%7B3%7D%2B4%20p%5E%7B2%7D-2%5Cright%29)
Distributive property: ![a(b+c)=ab + ac](https://tex.z-dn.net/?f=a%28b%2Bc%29%3Dab%20%2B%20ac)
![= p\left(p^{3}+4 p^{2}-2\right) -2\left(p^{3}+4 p^{2}-2\right)](https://tex.z-dn.net/?f=%3D%20p%5Cleft%28p%5E%7B3%7D%2B4%20p%5E%7B2%7D-2%5Cright%29%20-2%5Cleft%28p%5E%7B3%7D%2B4%20p%5E%7B2%7D-2%5Cright%29)
![= \left(p^{4}+4 p^{3}-2p\right) +\left(-2p^{3}-8 p^{2}+4\right)](https://tex.z-dn.net/?f=%3D%20%5Cleft%28p%5E%7B4%7D%2B4%20p%5E%7B3%7D-2p%5Cright%29%20%2B%5Cleft%28-2p%5E%7B3%7D-8%20p%5E%7B2%7D%2B4%5Cright%29)
![= p^{4}+4 p^{3}-2p-2p^{3}-8 p^{2}+4](https://tex.z-dn.net/?f=%3D%20p%5E%7B4%7D%2B4%20p%5E%7B3%7D-2p-2p%5E%7B3%7D-8%20p%5E%7B2%7D%2B4)
Arrange and add/subtract same powers.
![= p^{4}+(4 p^{3}-2p^{3})-8 p^{2}-2p+4](https://tex.z-dn.net/?f=%3D%20p%5E%7B4%7D%2B%284%20p%5E%7B3%7D-2p%5E%7B3%7D%29-8%20p%5E%7B2%7D-2p%2B4)
![= p^{4}+2 p^{3}-8 p^{2}-2p+4](https://tex.z-dn.net/?f=%3D%20p%5E%7B4%7D%2B2%20p%5E%7B3%7D-8%20p%5E%7B2%7D-2p%2B4)
Hence ![g(p) \cdot h(p) = p^{4}+2 p^{3}-8 p^{2}-2p+4](https://tex.z-dn.net/?f=g%28p%29%20%5Ccdot%20h%28p%29%20%3D%20p%5E%7B4%7D%2B2%20p%5E%7B3%7D-8%20p%5E%7B2%7D-2p%2B4)