Question

If you transform y = 2x^2 into y = 10x^2, which option below describes the effect of this transformation on the graph of the quadratic function along the y-axis?

The transformation stretches the graph by a factor of 5.
The transformation stretches the graph by a factor of 25.
The transformation shrinks the graph by a factor of 5.
The transformation shrinks the graph by a factor of 25.

Answer 1

the easiest way to determine this is to plug in some numbers into the equations.

lets say y = 2x^2 is A and y = 10x^2 is B

x y
A B
0 0 0
1 2 10
2 8 40
3 18 90

so you can see that equation B is growing much faster


the factor is given by the difference of the coefficients 2 and 10.

\(\sf difference=\dfrac{10}{2}=5\)