Heather is going to graph y = -3x^2 + 3. How is the parent graph transformed?
A) The parent graph is reflected over the x-axis, has a vertical stretch by a factor of 3 and is shifted up 3 units.
B) The parent graph is reflected over the y-axis, has a vertical stretch by a factor of 3 and is shifted up 3 units.
C) The parent graph is reflected over the y-axis, has a vertical stretch by a factor of 3 and is shifted left 3 units.
D) The parent graph is reflected over the x-axis, has a vertical compression by a factor of 3 and is shifted up 3 units.

Question

22-05-2018
Mathematics

contestada

Heather is going to graph y = -3x^2 + 3. How is the parent graph transformed?
A) The parent graph is reflected over the x-axis, has a vertical stretch by a factor of 3 and is shifted up 3 units.
B) The parent graph is reflected over the y-axis, has a vertical stretch by a factor of 3 and is shifted up 3 units.
C) The parent graph is reflected over the y-axis, has a vertical stretch by a factor of 3 and is shifted left 3 units.
D) The parent graph is reflected over the x-axis, has a vertical compression by a factor of 3 and is shifted up 3 units.

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carlosego carlosego · Answer 1 · 2018-06-01T16:03:35+02:00

For this case the parent function is given by:
y = x ^ 2
We apply the following transformations:
Reflections:
To graph y = -f (x), reflect the graph of y = f (x) on the x-axis. (Vertical reflection).
We have then:
y = -x ^ 2
Expansions and vertical compressions:
To graph y = a * f (x)
If a> 1, the graph of y = f (x) is expanded vertically by a factor a.
We have then:
y = -3x ^ 2
Vertical translations
Suppose that k> 0
To graph y = f (x) + k, move the graph of k units up.
We have then:
y = -3x ^ 2 + 3
Answer:
A) The parent graph is reflected over the x-axis, has a vertical stretch by a factor of 3 and is shifted up 3 units.

astha8579 astha8579 · Answer 2 · 2022-03-15T12:56:05+01:00

The transformation done on the parent graph is explained by: Option A) The parent graph is reflected over the x-axis, has a vertical stretch by a factor of 3 and is shifted up 3 units.

How does scaling works?

Suppose that you've got a measurement as 5 cm.

Now if you scale it, then you multiply it with 'x'. The final value is [tex]5x[/tex] cm.

That value [tex]x[/tex] by which we multiply the original measurement is called scale factor.

How does reflection across axis work?

When a graph is reflected along an axis, say x axis, then that leads the graph to go just in opposite side of the axis as if we're seeing it in a mirror.

If you study it more, you will find that its symmetric, thus each point is equidistant from the axis of reflection as that of the image of that point.

Thus, if you're reflecting a point (x,y) along x axis, then its [tex]x[/tex] abscissa will stay same but [tex]y[/tex] ordinates will negate. Thus (x,y) turns to (x, -y)

Similarly, if you're reflecting a point (x,y) along y axis, the resultant image of the point will be (-x,y)

How does origin shifting left or right of a graph works?

For a graph [tex]y = f(x)[/tex], the shift of [tex]a[/tex] units left is done by making y take values of original function [tex]a[/tex] units before,

thus, the shifted function will look like: [tex]y = f(x+a)[/tex]

Similarly, to shift a function [tex]a[/tex] units right, we subtract 'a' from the input so that the original function's values come 'a' units late.

The new shifted function will look like: [tex]y = f(x-a)[/tex]

Now, the original function given in the considered case(missing in the question) is [tex]y = x^2[/tex]

The function Heather is going to graph is [tex]y = -3x^2 + 3[/tex]

You see, the term [tex]x^2[/tex] is multiplied with [tex]-3[/tex]. We can take it in 2 steps, as:

First the graph of [tex]y = x^2[/tex] is scaled by 3, thus, resulting in [tex]y= 3x^2[/tex]

The graph of the function is then reflected across x-axis (as the value of y becomes negative), thus, resulting in [tex]y = -3x^2[/tex] (we can take it as: first reflecting, then scaling too).

Since the scaling affects the y output, which is plotted vertically, therefore, it is also called vertical stretch.

Now, 3 is added to each output, thus, it means the scaled and reflected function is then taken 3 units up in vertical axis(as, y-axis values are plotted vertically). Thus, resulting function becomes [tex]y = -3x^2 + 3[/tex]

Therefore, the transformation done on the parent graph is explained by: Option A) The parent graph is reflected over the x-axis, has a vertical stretch by a factor of 3 and is shifted up 3 units.

Learn more about transformation of functions here:

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