Question

The parent function of a quadratic equation is vertically stretched by a factor of 2, then translated 4 units left and one unit down

Answer 1

`f`

Explanation:

Given

`f(x) = x^2` --- the quadratic function

Vertically stretched by 2

Translation:
`4\ units` left and
`1\ unit` down

Required

Determine the new function

`f(x) = x^2`

The rule for vertical stretch is:

`(x,y) \to (x,ay)`

In this case:

`a = 2`

So, we have:

`f(x) = x^2`

`f'(x) = a * f(x)`

`f'(x) = a * x^2`

Substitute:
`a = 2`

`f'(x) = 2 * x^2`

`f'(x) =2x^2`

Translation: 4 units left

The rule is:

`(x,y) \to (x - c,y)`

In this case:
`c =4`

So, we have:

`f`

Translation: 1 unit down

The rule is:

`(x,y) \to (x,y-d)`

In this case,
`d=1`

So, we have:

`f`

`f`