Answer:
C 470
Step-by-step explanation:
To identify the grpah correspondig to the given function find the zeros of the function (use the quadratic formula):
![\begin{gathered} f(x)=\frac{1}{2}x^2+2x-6 \\ \\ x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ \\ a=\frac{1}{2} \\ \\ b=2 \\ c=-6 \\ \\ \\ x=\frac{-2\pm\sqrt[]{2^2-4(\frac{1}{2})(-6)}}{2(\frac{1}{2})} \\ \\ x=\frac{-2\pm\sqrt[]{4-(-12)}}{1} \\ \\ x=\frac{-2\pm\sqrt[]{16}}{1} \\ \\ x=\frac{-2\pm4}{1} \\ \\ x_1=-2+4=2 \\ x_2=-2-4=-6 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20f%28x%29%3D%5Cfrac%7B1%7D%7B2%7Dx%5E2%2B2x-6%20%5C%5C%20%20%5C%5C%20x%3D%5Cfrac%7B-b%5Cpm%5Csqrt%5B%5D%7Bb%5E2-4ac%7D%7D%7B2a%7D%20%5C%5C%20%20%5C%5C%20a%3D%5Cfrac%7B1%7D%7B2%7D%20%5C%5C%20%20%5C%5C%20b%3D2%20%5C%5C%20c%3D-6%20%5C%5C%20%20%5C%5C%20%20%5C%5C%20x%3D%5Cfrac%7B-2%5Cpm%5Csqrt%5B%5D%7B2%5E2-4%28%5Cfrac%7B1%7D%7B2%7D%29%28-6%29%7D%7D%7B2%28%5Cfrac%7B1%7D%7B2%7D%29%7D%20%5C%5C%20%20%5C%5C%20x%3D%5Cfrac%7B-2%5Cpm%5Csqrt%5B%5D%7B4-%28-12%29%7D%7D%7B1%7D%20%5C%5C%20%20%5C%5C%20x%3D%5Cfrac%7B-2%5Cpm%5Csqrt%5B%5D%7B16%7D%7D%7B1%7D%20%5C%5C%20%20%5C%5C%20x%3D%5Cfrac%7B-2%5Cpm4%7D%7B1%7D%20%5C%5C%20%20%5C%5C%20x_1%3D-2%2B4%3D2%20%5C%5C%20x_2%3D-2-4%3D-6%20%5Cend%7Bgathered%7D)
As the zeros are 2 and -6 the graph cross the x-axis in x=2 and x=-6
<h2>Answer: D</h2>
7x^3 + 9x^2 -3x -8
***************************************************************
Given this equation:
![f(x)=301+29^{-0.5x}](https://tex.z-dn.net/?f=f%28x%29%3D301%2B29%5E%7B-0.5x%7D)
That represents t<span>he height of a tree in feet over (x) years. Let's analyze each statement according to figure 1 that shows the graph of this equation.
</span>
The tree's maximum height is limited to 30 ft.
As shown in figure below, the tree is not limited, so this statement is false.
<span>
The tree is initially 2 ft tall
The tree was planted in x = 0, so evaluating the function for this value, we have:
</span>
![f(0)=301+29^{-0.5(0)}=301+1=302ft](https://tex.z-dn.net/?f=f%280%29%3D301%2B29%5E%7B-0.5%280%29%7D%3D301%2B1%3D302ft)
<span>
<span>So, the tree is initially
![\boxed{302ft}](https://tex.z-dn.net/?f=%5Cboxed%7B302ft%7D)
tall.
</span>
Therefore this statement is false.
</span>
Between the 5th and 7th years, the tree grows approximately 7 ft.
<span>
if x = 5 then:
</span>
![f(5)=301+29^{-0.5(5)}=301ft](https://tex.z-dn.net/?f=f%285%29%3D301%2B29%5E%7B-0.5%285%29%7D%3D301ft)
<span>
</span>if x = 7 then:
![f(7)=301+29e^{0.5(7)}=301ft](https://tex.z-dn.net/?f=f%287%29%3D301%2B29e%5E%7B0.5%287%29%7D%3D301ft)
So, between the 5th and 7th years the height of the tree remains constant
:
![\Delta=f(7)-f(5)=301-301=0ft](https://tex.z-dn.net/?f=%5CDelta%3Df%287%29-f%285%29%3D301-301%3D0ft)
This is also a false statement.
<span>
After growing 15 ft, the tree's rate of growth decreases.</span>
It is reasonable to think that the height of this tree finally will be 301ft. Why? well, if x grows without bound, then the term
![29^{-\infty}](https://tex.z-dn.net/?f=29%5E%7B-%5Cinfty%7D)
approaches zero.
Therefore this statement is also false.
Conclusion: After being planted this tree won't grow.
15 hours. So maybe call an Uber.