Question

Y=1/4x^2, what effect does the number 1/4 on the graph, as compared to the graph of the function y=x^2?

Answer 1

It shrinks the graph vertically to 1/4 its original height ⇒ 1st answer

Explanation:

* Lets revise the vertical stretch and shrink

- A vertical stretching is the stretching of the graph away from the

x-axis

- If k > 1, the graph of y = k • f(x) is the graph of f(x) vertically

stretched by multiplying each of its y-coordinates by k

- A vertical shrink is the squeezing of the graph toward

the x-axis.

- If 0 < k < 1 (a fraction), the graph of y = k • f(x) is the graph of f(x)

vertically shrank by multiplying each of its y-coordinates by k

* Now lets solve the problem

∵ The function
`y=(1)/(4)x^(2)`

∵ The parent function is y = x²

- The parent function y = x² is multiplied by a factor

∴ The parent function is stretched or shrank vertically

∵ The factor is
`(1)/(4)`

∵
`0<(1)/(4)<1`

∴ The parent function shrinks vertically by scale factor
`(1)/(4)`

∵ When the graph shrank vertically, then each y-coordinates oo the

point lie on the graph multiplied by 1/4

- That means the height of the graph is 1/4 of the height of the original

∴ The answer is the graph shrank vertically to 1/4 its original height

* It shrinks the graph vertically to 1/4 its original height