Question

Graph the following function and identify any shifts, stretches, and symmetry and x and y intercepts:

Answer 1

Shifts:

Shifted three units right and two units up to match the blue parabola

Stretches:

It doesn't have any stretches

Symmetry:

$x=3$

x and y intercepts:

x intercpets: It has no x-intercepts

y-intercepts: (0, 11)

Explanation:

The pattern of the quadratic function is:

$f(x)=x^2$

Whose graph is shown below as the red parabola.

So here we need to identify some characteristics of:

$y = f(x) = (x - 3)^2 + 2$

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:

$y=f(x)$

We have the following transformations:

$y=h(x)=f(x+c)+k \\ \\ \\ \bullet \ c>0 \ Shift \ f(x) \ c \ units \ to \ the \ left \\ \\ \bullet \ c0 \ Shift \ f(x) \ k \ units \ up \\ \\ \bullet \ k$

On the other hand, the blue graph has neither stretches nor x intercepts. Finally, its axes of symmetry is $x=3$. The y-intercept is (0, 11) is indicated in the figure.

Learn more:

Shifting graphs: brainly.com/question/10010217

#LearnWithBrainly