The vertex is the high point of the curve, (2, 1). The vertex form of the equation for a parabola is .. y = a*(x -h)^2 +k . . . . . . . for vertex = (h, k)
Using the vertex coordinates we read from the graph, the equation is .. y = a*(x -2)^2 +1
We need to find the value of "a". We can do that by using any (x, y) value that we know (other than the vertex), for example (1, 0). .. 0 = a*(1 -2)^2 +1 .. 0 = a*1 +1 .. -1 = a
Now we know the equation is .. y = -(x -2)^2 +1
_____ If we like, we can expand it to .. y = -(x^2 -4x +4) +1 .. y = -x^2 +4x -3
========= An alternative approach would be to make use of the zeros. You can read the x-intercepts from the graph as x=1 and x=3. Then you can write the equation as .. y = a*(x -1)*(x -3) Once again, you need to find the value of "a" using some other point on the graph. The vertex (x, y) = (2, 1) is one such point. Subsituting those values, we get .. 1 = a*(2 -1)*(2 -3) = a*1*-1 = -a .. -1 = a Then the equation of the graph can be written as .. y = -(x -1)(x -3) In expanded form, this is .. y = -(x^2 -4x +3) .. y = -x^2 +4x -3 . . . . . . same as above
