Answer:
Please refer to the images attached below.
Step-by-step explanation:
Quadratic Functions are functions of degree 2. The graph of any quadratic function is a parabola that has a vertex and axis of symmetry.
Some Properties of Graph Translations
1. y=a(x-h)^2+ky=a(x−h)
2
+k
This means that the new function is translated h units to the right and k units going up.
2. y=a(x-h)^2-ky=a(x−h)
2
−k
This means that the new function is translated h units to the right and k units going down.
3. y=a(x+h)^2+ky=a(x+h)
2
+k
This means that the new function is translated h units to the left and k units going up.
4. y=a(x+h)^2-ky=a(x+h)
2
−k
This means that the new function is translated h units to the left and k units going down.
First, let's graph the function y=3x^2+3y=3x
2
+3 . The vertex is at the point (0,3)(0,3) . Please refer to Figure 1 below.
Now, start from the vertex of the first function, (0,3)(0,3) , as you notice that the function y=3(x-3)^2+1y=3(x−3)
2
+1 is 3 units translation to right and one unit translation going up. This means that the new vertex is the point (3,1)(3,1) .Please refer to Figure 2.
For the function, y=3(x+3)^2-1y=3(x+3)
2
−1 , start from the vertex of the first function, (0,3)(0,3) , then make a translation of 3 units to the left and a translation of 1 unit down. This gives us a new vertex of (-1, -3)(−1,−3) . Please refer to Figure 3.
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To learn more about quadratic functions, go to
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Step-by-step explanation:
<em>FOLLOW</em><em> </em><em>ME </em><em>OKAY </em><em />
<em>I </em><em>WILL</em><em> FOLLOW</em><em> </em><em>YOU</em><em> </em><em>BACK</em><em> </em><em />
