Answer:
Step-by-step explanation:
We will use the work form of a quadratic to determine what a is...in fact we will write the equation for the whole thing in the process, because it's part of solving for a.
y = ±|a|(x - h)² + k
where x and y are from a coordinate point on the graph, h and k are the coordinates of the vertex, the absolute value of a indicates how steep or flat the graph is compared to the parent graph, and the ± is because a positive parabola opens up and a negative one opens upside down.
The vertex is (0, 9) and the coordinate point I chose to use is (3, 0). Filling those in and solving for a:
0 = ±|a|(3 - 0)² + 9 and
0 = ±|a|(3)² + 9 and
-9 = ±|a|9 and
-1 = ±|a| so a = 1. Because this is an upside down parabola the negative is out front, but a is independent of it. The correct choice is C. The quadratic function is
[tex]y=-x^2+9[/tex] or in more detailed form:
[tex]y=-(x-0)^2+9[/tex]
