46. Give the domain and range of the quadratic function with the following properties.

Question

Vertex at (-6, 9)
Passes through (-4, 13)
Opens up

Answer 1

An equation of a parabola with vertex (h,k) and which opens either upward or downward is y = A(x-h)²+k.  If A>0, the parabola opens upward.  If A<0, the parabola opens downward.  

 

Since the vertex is (-6,9), we have y = A(x+6)² + 9

 

Since the point (-4,13) is on the graph, 13 = A(-4+6)²  + 9

 

                                                          13 = 4A + 9

 

                                                          4A = 4     So, A = 1

 

Therefore, y = (x+6)² +9.

 

Since the parabola opens upward (A>0), the vertex is the lowest point of the graph.

 

    Range = set of all possible values of y = [9,∞)

 

    Domain = set of all possible values of x = (-∞, ∞)