I need help Equation

Question

The graph of a parabola is represented by the equation y=ax² where a is a positive integer . If a is multiplied by 2 , the new parabola will become

Answer 1

Notice that for a specific value of x, the y-coordinate will be twice as large. For example, if x=3 then the two y-coordinates are

y = a(3)^2 = a9 (usually written as 9a)

y=2a(3)^2 = 2a9 = 18a (notice that this is 2 times 9a).

Since all the y-coordinates will be twice as big, the graph of the new parabola will be twice as far from the x axis. That is, it's a vertical stretch.

Answer 2

In general, say you have function g(x) and have the following transformations:

a*g(x - b) + d

a = vertical stretch / compression

b = horizontal shift

d = vertical shift



In this problem, multiplying a by 2 will vertically stretch the graph by a factor of 2.