Shifts:
Shifted three units right and two units up to match the blue parabola
Stretches:
It doesn't have any stretches
Symmetry:
[tex]x=3[/tex]
x and y intercepts:
x intercpets: It has no x-intercepts
y-intercepts: (0, 11)
Explanation:
The pattern of the quadratic function is:
[tex]f(x)=x^2[/tex]
Whose graph is shown below as the red parabola.
So here we need to identify some characteristics of:
[tex]y = f(x) = (x - 3)^2 + 2[/tex]
Whose graph is shown below as the blue parabola.
As you can see, the blue parabola is a transformation of the red parabola. The rule is as follows:
- The red parabola has been shifted three units right and two units up to match the blue parabola.
This is so because, for any function:
[tex]y=f(x)[/tex]
We have the following transformations:
[tex]y=h(x)=f(x+c)+k \\ \\ \\ \bullet \ c>0 \ Shift \ f(x) \ c \ units \ to \ the \ left \\ \\ \bullet \ c<0 \ Shift \ f(x) \ c \ units \ to \ the \ right \\ \\ \bullet \ k>0 \ Shift \ f(x) \ k \ units \ up \\ \\ \bullet \ k<0 \ Shift \ f(x) \ k \ units \ down[/tex]
On the other hand, the blue graph has neither stretches nor x intercepts. Finally, its axes of symmetry is [tex]x=3[/tex]. The y-intercept is (0, 11) is indicated in the figure.
Learn more:
Shifting graphs: https://brainly.com/question/10010217
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