Answer-
The value of a is -2
Solution-
The vertex form of parabola-
\(y=a(x-h)^2+k\)
Where, vertex is at (h, k)
Given that the vertex is at (6, 2), so equation would be
\(y=a(x-6)^2+2\)
As the y intercept is the point which lies on the parabola, so it must satisfy the parabola equation.
\(\Rightarrow -70=a(0-6)^2+2\)
\(\Rightarrow -70-2=a(-6)^2\)
\(\Rightarrow a(6)^2=-72\)
\(\Rightarrow 36a=-72\)
\(\Rightarrow a=-2\)
