Question

Which function transforms the graph of
y=x^2
so that it is first shifted down 4 units and is then reflected across the y-axis?

Answer 1

Answer on Question #78191 – Math – Trigonometry

Question

Which function transforms the graph of

$$y = x^2$$

so that it is first shifted down 4 units and is then reflected across the y-axis?

Solution

Since the function has the form

$$y = x^2$$

, the function

$$y = x^2 - 4$$

is shifted 4 units below. Due to the fact that the function is quadratic, then its reflection with respect to the y axis will be the same function because

$$y = (-x)^2 - 4 = x^2 - 4$$

.

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