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Write an equation of the parabola that has the same shape as the graph of f(x)= 3x², but with the point (3,-4) as the vertex.

User Niels Heisterkamp
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1 Answer

19 votes
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Answer: y = 3(x-3)^2-4

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Step-by-step explanation:

The graph of y = 3x^2 has (0,0) as the vertex.

To move from (0,0) to (3,-4) we will shift 3 units right and 4 units down.

Therefore, we will have y = 3(x-3)^2-4 as the answer

It is of the form y = a(x-h)^2+k with (h,k) being the vertex.

The 'a' value out front vertically stretches or compresses the parabola. Also if a > 0, then the parabola opens upward; or if a < 0, then the parabola opens downward.

We keep the same value of 'a' so that both parabolas have the same shape.

User ComSubVie
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