The function is ![y = (x +2)^2 + 5.](https://tex.z-dn.net/?f=y%20%3D%20%28x%20%2B2%29%5E2%20%2B%205.)
we use the vertex form of the quadratic equation
We have given a graph,
<h3>What is the vertex form of the quadratic equation?</h3>
y = a(x - h)^2 + k.
Therefore the vertex of the given graph is
See the vertex at (-2, 5)
Since the general way to write the vertex is (h, k), we compare (h, k) to (-2, 5).
![y = a(x - (-2))^2 + 5.\\y=a(x+2)^2+5......(1)](https://tex.z-dn.net/?f=y%20%3D%20a%28x%20-%20%28-2%29%29%5E2%20%2B%205.%5C%5Cy%3Da%28x%2B2%29%5E2%2B5......%281%29)
Now we have given that (-4,1) use this value in the above equation so we get,
![(1)=a(-4+2)^2+5](https://tex.z-dn.net/?f=%281%29%3Da%28-4%2B2%29%5E2%2B5)
![1=a(-2)^2+5](https://tex.z-dn.net/?f=1%3Da%28-2%29%5E2%2B5)
![1=4a+5](https://tex.z-dn.net/?f=1%3D4a%2B5)
![1-5=4a](https://tex.z-dn.net/?f=1-5%3D4a)
![-4=4a](https://tex.z-dn.net/?f=-4%3D4a)
![a=-4/4](https://tex.z-dn.net/?f=a%3D-4%2F4)
![a=-1](https://tex.z-dn.net/?f=a%3D-1)
Using the value of an in equation (1) we get,
Therefore the function is ![y = (x +2)^2 + 5.](https://tex.z-dn.net/?f=y%20%3D%20%28x%20%2B2%29%5E2%20%2B%205.)
To learn more about the function visit:
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The correct answer is 256.
The surface area of the design is 5
Answer:
Step-by-step explanation:
To solve this you just do 14 - 52 then you get 38. Make sure to check your work. 38 + 14 = 52.