quadratic ques

Question

write the standard for, of a quadratic function that has roots at (3,0) and (-5,0) and has been stretched vertically by a factor of 4 

Answer 1

The equation must have the factors (x - 3) and (x + 5) to have those two roots. To allow for the vertical stretch factor, you can use:

 

f(x) = a(x - 3)(x + 5) with a = 4:

 

f(x) = 4(x - 3)(x + 5) = 4(x² + 2x - 15) = 4x² + 8x - 60.

 

If this is what you need, okay. If you need the standard form (vertex form), you must complete the square:

 

f(x) = 4(x² + 2x + 1) - 60 - 4 = 4(x + 1)² - 64 .

 

Let me know if this works for you.