Question

In the xy-plane, if the parabola with equation y=a(x+2)^(2)-15 passes through (1,3), what is the value of a ?

Answer 1

To find the value of 'a' in the equation y = a(x+2)^2 - 15, substitute the coordinates (1,3) into the equation and solve for a. The calculated value of a is 2.

Step-by-step explanation:

The student is asking to find the value of a in the parabolic equation y = a(x+2)2 - 15 given that the parabola passes through the point (1,3). To find a, substitute x with 1 and y with 3 in the equation and solve for a.

First, plug in the coordinates:

3 = a(1+2)2 - 15

Next, simplify and solve the equation:

1. 3 = a(3)2 - 15
2. 3 = 9a - 15
3. 18 = 9a
4. a = 2

Therefore, the value of a is 2.