Question

In the function y-1=(4x)^2+7 , what effect does the number 4 have on the graph, as compared to the graph of y=x^2 ?

Answer 1

Points (1,3) are given in the form of  (x,y)
 So,

 (x,y) = (1,3)

 which shows that

 x = 1 and y = 3

So,
   y = 3x + b
  3 = 3(1) + b
 
if you would solve for  b you will get
 b= 0

Answer 2

The constant terms only translate the function upward or donward.

Here the focus is in the coefficient that multiplies the term x^2.

The effect is to stretch the graph vertically.

In y=x^2, when x = 1 y =1 and when x=2 y = 4

In y=(4x)^2 , when x = 1 y = 16 and when x =2 y=16

Then the factor of stretching vertically is 16.

Also you can see the transformation from the point of view of the horizontal axis.

For the function y =x^2, when y is 16 x = 4,
For the function y = (4x)^2, when y is 16 x = 1,

For the funcion y = x^2, when y = 64 x = 8
For the function y =(4x)^2, when y = 64 x =2

Then x is multiplied by a factor of 1/4, which means that the answer is "
It shrinks the graph horizontally to 1/4 the original width"

That is why the resu