Since the table represented a quadratic function, we obtained a parabola. Notice that we can identify the coordinates of its vertex.
Because we know the vertex, we can write the equation in a vertex form.
f(x)= a(x- h)^2+ k
In this expression, a, h, and k are either positive or negative constants. In our case the vertex is ( 4, 5), so we have h= 4 and k= 5. We can use these values to partially write our equation.
f(x)= a(x-( 4))^2+( 5)
⇕
f(x)= a(x-4)^2+5
To find the value of a, we will use one of the given points that is not the vertex. Let's take ( 2, - 3). Since this point is on the curve, it satisfies its equation. Therefore, to find the value of a, we can substitute 2 for x and - 3 for f(x) and simplify.
