Question

the graph of a quadratic function (a parabola) has x-intercepts -1 and 3 and a range consisting of all numbers less than or equal to 4. determine an expression for the function

Answer 1

factored form
y = a(x+1)(x-3)
max = 4
find x_coord of vertex
Because of symmetry, vertex is exactly in the middle of x=-1 and x=3
(-1+3)/2 = 2/2 = 1
vertex: (1,4)
plug in these x,y values to solve for a
4 = a(1+1)(1-3)
4=a(2)(-2)
4 = -4a
-1 = a
Final equation:
y = -(x+1)(x-3)

Answer 2

thank you!

Answer 3

no problem
hope that made sense