Question

Write the equation of the parabola that has the vertex at point (2,7) and passes through the point (−1,3).

Answer 1

Step One
Use the vertex to determine the basic equation for the parabola.

y = a(x - 2)^2 + 7 Notice the sign change for x. I have provided a graph to show how this would look with a = 1 (in red.)

What it means is the  2 has to be minus in order that the vertex will shift 2 units in the x direction.

Step Two
Use the point to solve for a.
y = a(x - 2)^2 + 7
When x = - 1
Then y = 3

3 = a(-1 - 2)^2 + 7                combine -1 with - 2
3 = a (-3)^2 + 7
3 = 9a + 7                            Subtract 7 from both sides
3 - 7 = 9a
-4 = 9a                                 Divide by 9.
a = -4/9 
or                                
a = - 0.4444

y = -0.4444(x + 2)^2 + 7 <<<<< answer
y = - 4/9 (x + 2)^2 + 7

Note: if you have choices, list them please.

Note: The red graph is y = (x - 2)^2 + 7 ; a = 1
The blue graph is y = - 4/9(x - 2)^2 + 7 ; a = - 0.44444

You should notice that the a does 3 things to the graph. Before you read the answer, what are those three things? The answer is in the comments.