Find a possible formula for the quadratic function whose graph has a x intercepts 2 and 4 and y intercept 22

Question

 

 

 

Find a possible formula for the quadratic function whose graph has  a x intercepts 2 and 4  and y intercept 22

 

 

Answer 1

Since 2 and 4 are x-intercepts, x-2 and x-4 are factors of the quadratic function.  

 

The quadratic function has the form f(x) = a(x-2)(x-4).  Since f(0) =22,   

a(0-2)(0-4) = 22.

 

So, 8a = 22   a = 11/4

 

f(x) = (11/4)(x-2)(x-4)

 

 

Answer 2

y = a(x-2)(x-4) could be it, because obviously y = 0 if x = 2 or x = 4.

 

Also, because of y-intercept (0,22), we have 22 = a(0-2)(0-4);  22 = 8a;  a = 11/4.

 

You take it from here!