Find $b$ and $c$ so that $y=-4 x^{2}+b x+c$ has vertex $(2,-3)$. \[ c= \] Question Help: $\square$ Video Submit Question Jump to Answer

Step 1 ：The vertex form of a quadratic equation is given by \(y=a(x-h)^{2}+k\), where \((h,k)\) is the vertex of the parabola.

Step 2 ：Given that the vertex is \((2,-3)\), we can rewrite the given equation in vertex form as follows: \(y=-4(x-2)^{2}-3\).

Step 3 ：Expanding this equation gives: \(y=-4(x^{2}-4x+4)-3\), which simplifies to \(y=-4x^{2}+16x-16-3\), and further simplifies to \(y=-4x^{2}+16x-19\).

Step 4 ：Comparing this with the original equation \(y=-4x^{2}+bx+c\), we can see that \(b=16\) and \(c=-19\).

Step 5 ：So, the final answer is \(\boxed{b=16, c=-19}\).