Find a polynomial function of degree 2 whose x-intercepts are -1 and 5 and whose range is (-infinity,9].

Question

I need to know what the polynomial is and the vertex of the polynomial is.

Answer 1

A parabola opening downward with x-coordinate of vertex halfway between x = -1 and x = 5  and with y-coordinate 9 would work.  

 

So, vertex = (2, 9)

 

Equation of parabola:  y = A(x+1)(x-5).  Find A so that y = 9 when

x = 2

 

9 = A(3)(-3)    A = -1

 

y = -(x+1)(x-5)

 

y = -(x² - 4x - 5)

 

y = -x² + 4x + 5