Question

Write a transformation of a quadratic function with a vertical stretch by a factor of 2, followed by a horizontal shift of 3 units to the left and 5 units down.show workkkk!!!

Answer 1

The standard form of a quadratic function presents the function in the form

`f(x)=a(x-h)^2+k`

where (h, k) is the vertex.

The standard form is useful for determining how the graph is transformed from the graph of y = x^2. The figure below is the graph of this basic function.

You can represent a horizontal (left, right) shift of the graph of

by adding or subtracting a constant, h, to the variable x, before squaring. Here h = -3

`y=(x+3)^2`

The magnitude of a indicates the stretch of the graph. a = 2

`y=2(x+3)^2`