3(13-2a)=-3+a
39-6a=-3+a
42=7a
a=6
Point slope form = y - b= m ( x - a )
where y and x stay the same
m is the slope
and (a, b) (any coordinate on the graph)
based on the point (5, -7)
Y - (-7) = -3 (x - 5)
however, the - cancels out the negative 7 making I positive
Y + 7 = -3(x - 5)
![y = -\frac{1}{9}(x - 1)^2 - 6](https://tex.z-dn.net/?f=y%20%3D%20-%5Cfrac%7B1%7D%7B9%7D%28x%20-%201%29%5E2%20-%206)
Step-by-step explanation:
The vertex form of the equation for a parabola is given by
![y = a(x - h)^2 + k](https://tex.z-dn.net/?f=y%20%3D%20a%28x%20-%20h%29%5E2%20%2B%20k)
where (h, k) are the coordinates of the parabola's vertex. Since the vertex is at (1, -6), we can write the equation as
![y = a(x - 1)^2 - 6](https://tex.z-dn.net/?f=y%20%3D%20a%28x%20-%201%29%5E2%20-%206)
Also, since the parabola passes through (4, -7), we can use this to find the value for a:
![-7 = a(4 - 1)^2 - 6 \Rightarrow -7 = 9a - 6](https://tex.z-dn.net/?f=-7%20%3D%20a%284%20-%201%29%5E2%20-%206%20%5CRightarrow%20-7%20%3D%209a%20-%206)
or
![a = -\frac{1}{9}](https://tex.z-dn.net/?f=a%20%3D%20-%5Cfrac%7B1%7D%7B9%7D)
Therefore, the equation of the parabola is
![y = -\frac{1}{9}(x - 1)^2 - 6](https://tex.z-dn.net/?f=y%20%3D%20-%5Cfrac%7B1%7D%7B9%7D%28x%20-%201%29%5E2%20-%206)
See attached picture for answer: