Find $\mathrm{b}$ and $\mathrm{c}$ so that $y=14 x^{2}+b x+c$ has vertex $(-1,4)$
\[
b=
\]
\[
c=
\]

Answer

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Answer

Final Answer: The coefficients $b$ and $c$ are $\boxed{28}$ and $\boxed{18}$ respectively.

Steps

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

Step 2 ：In this case, we know that $a=14$, $h=-1$ and $k=4$.

Step 3 ：We can expand this equation to get it in the form $y=ax^{2}+bx+c$.

Step 4 ：Doing so, we get $y = 14*(x + 1)^{2} + 4$.

Step 5 ：Expanding this equation, we get $y = 14*x^{2} + 28*x + 18$.

Step 6 ：Comparing coefficients, we find that $b = 28$ and $c = 18$.

Step 7 ：Final Answer: The coefficients $b$ and $c$ are $\boxed{28}$ and $\boxed{18}$ respectively.