Question

Given the following translated function , state the translations that have occurred and write the translated equation Toolkit function :y=x^2

Answer 1

Solution

Step 1

Write the function:

$y\text{ = x}^2$

Step 2

The function is reflected over the x-axis

f(x) to −f (x) reflects the function in the x-axis (that is, upside-down).

$y\text{ = -x}^2$

Step 2

Rule for vertical shift

When you shift f(x) vertically upward by b units, it becomes f (x) + b shifts the function b units upward.

$y\text{ = -x}^2+1$

y is shift 1 unit upward.

Final step

The finally the function is shift 2 units right using the rule below

f(x) shifted b units to the right to form f (x − b) shifts the function b units to the right.

$y\text{ = -\lparen x-2\rparen}^2+1$

Final answer

$y\text{ = -\lparen x-2\rparen}^2+1$