# How do you write the quadratic function in vertex form given vertex (0,0) and point (-2,-12)?

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To write the quadratic function in vertex form given the vertex (0,0) and point (-2,-12), follow these steps:

- Use the vertex form of a quadratic function: ( f(x) = a(x - h)^2 + k ), where (h, k) is the vertex.
- Substitute the vertex coordinates (0,0) into the equation: ( f(x) = a(x - 0)^2 + 0 ).
- This simplifies to ( f(x) = ax^2 ).
- Now, substitute the coordinates of the given point (-2,-12) into the equation: ( -12 = a(-2)^2 ).
- Solve for 'a': ( -12 = 4a ), so ( a = -3 ).
- Finally, substitute 'a' back into the equation: ( f(x) = -3x^2 ).

So, the quadratic function in vertex form is ( f(x) = -3x^2 ).

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