Find the general form of the quadratic function that has a vertex of $$ (-2,-1) $$ and a point on the graph $$ (4,35) $$.

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We start with the vertex form of a quadratic function:
$$
f(x)=a(x-h)^2+k
$$
Since the vertex is $$(-2,-1)$$, we have $$h=-2$$ and $$k=-1$$, thus:
$$
f(x)=a(x+2)^2-1
$$
Next, we use the point $$(4,35)$$ which lies on the graph:
$$
35=a(4+2)^2-1
$$
Simplify inside the parentheses:
$$
35=a(6)^2-1
$$
$$
35=a(36)-1
$$
Add $$1$$ to both sides:
$$
36=36a
$$
Solve for $$a$$:
$$
a=1
$$
Substitute $$a=1$$ back into the function:
$$
f(x)=(x+2)^2-1
$$
Expanding the square:
$$
f(x)=x^2+4x+4-1
$$
Simplify:
$$
f(x)=x^2+4x+3
$$
Thus, the general form of the quadratic function is:
$$
\boxed{f(x)=x^2+4x+3}
$$
The quadratic function is $$ f(x) = x^2 + 4x + 3 $$.

Find the general form of the quadratic function that has a vertex of and a point on the graph .

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