Answer:
f(x) = (-3/4)x^2 + 3
Explanation:
First, look at the vertex to see if it intersects the y-axis. It does, which is good, because it makes your job a lot easier by making your equation to fill out y = ax + b. Your b is the y value of your vertex, which in this case is 3. Then, your a is the amount you're multiplying plain old x^2 by to get your values (before adding 3). Because the graph is pointing down, you know right away that it's going to be negative. Also, going to the left or right by 2 (the points you are given) from the vertex gives you a result of going down 3. Normally this would mean you move up by 4 (again, from the vertex), so what do you need to multiply 4 by to get -3? -3/4, so that's your a. This makes your equation (y OR) f(x) = (-3/4)x^2 + 3
I hope I didn't make any mistakes reading your graph! I had a bit of difficulty with it unfortunately.