Question

why write a quadratic function whose graph has the given characteristics vertex :(2,3) point on graph (0,-1)

Answer 1

Answer:

f(x) = -(x -2)² +3

Step-by-step explanation:

We can fill in the vertex (h, k) values immediately in the vertex form ...

... f(x) = a(x -h)² +k

To find the value of a, we solve the equation for a at some point other than the vertex. The given point is (0, -1), so we can use that:

... -1 = a(0 -2)² +3

... -4 = 4a . . . . . . . . . subtract 3, simplify

... -1 = a . . . . . . . . . . . divide by 4

Now, we know the function is ...

... f(x) = -(x -2)² +3