A vertical stretch of a curve by a scale factor "k" is represented by multiplying the entire function by "k." In this case, the scale factor is "k."
The original equation of the curve is:
y = 3x^2 + x + 5x - 5
To perform a vertical stretch with a scale factor "k," the equation becomes:
y = k(3x^2 + x + 5x - 5)
Now, distribute "k" into the terms within the parentheses:
y = 3kx^2 + kx + 5kx - 5k
So, the equation of the new curve after the vertical stretch by a scale factor "k" is:
y = 3kx^2 + (k + 5k)x - 5k
You can simplify this further if needed.
Hope this helps! :)