A parabola is a curve with a focus and a directrix. The focus is any point is at an equal distance while the directrix is a fixed line. The vertex of the parabola is (2,1), the two points to the right are (3,4) & (4,13) while the two points to the left are (1,4) & (0,13).
Given that:
[tex]y = 3(x - 2)^2 + 1[/tex]
A parabola is represented as:
[tex]y = a(x - h)^2 + k[/tex]
Where:
[tex]Vertex = (h,k)[/tex]
So, by comparison; the vertex of the function is:
[tex]Vertex = (2,1)[/tex]
To plot two points to the right, we select x values greater than 2.
Let: [tex]x = 3[/tex]
So, we have:
[tex]y = 3(x - 2)^2 + 1[/tex]
[tex]y = 3(3 - 2)^2 + 1[/tex]
[tex]y = 4[/tex]
Let [tex]x = 4[/tex]
[tex]y = 3(x - 2)^2 + 1[/tex]
[tex]y = 3(4 - 2)^2 + 1[/tex]
[tex]y =13[/tex]
To plot two points to the left, we select x values less than 2.
Let: [tex]x=1[/tex]
So, we have:
[tex]y = 3(x - 2)^2 + 1[/tex]
[tex]y = 3(1 - 2)^2 + 1[/tex]
[tex]y = 4[/tex]
Let [tex]x = 0[/tex]
[tex]y = 3(x - 2)^2 + 1[/tex]
[tex]y = 3(0 - 2)^2 + 1[/tex]
[tex]y =13[/tex]
In conclusion:
- The vertex of the parabola is (2,1)
- The two points on the right are (3,4) and (4,13)
- The two points on the left are (1,4) and (0,13)
See attachment for graph
Read more about parabola at:
https://brainly.com/question/20333425
