Write the equation of a quadratic functino whose zeroes are -1, 3 and a range consisting of all numbers less than or equal to 4

Question

i know that (x+1)(x-3) is what is true and that it is also a flipped parabola to fit the range, but how do i get my parabola's vertex to be on 4?

Answer 1

Since the zeros are -1 and 3, the points (-1,0) and (3,0) are on the graph.  

 

By the symmetry of a parabola, the x-coordinate of the vertex is 1.

 

Since the range is (-∞,4], we are looking for a parabola opening downward with vertex (1,4).

 

Equation has the form y = a(x-1)² + 4

 

Since the point (3,0) lies on the graph, 0 = a(3-1)² + 4

 

                                                        4a = -4     a = -1

 

Equation:  y = -1(x-1)² + 4

 

               y = -(x² - 2x + 1) + 4

 

               y = -x² + 2x + 3

 

 

Answer 2

Good start!

 

4 ≥ (x+ 1)(x - 3)