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Write a quadratic function in vertex form that has a verte through the point (3,10).

33. Write a quadratic function in vertex form that has a verte through the point (3,10) (3,10) .

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Full solution

Q. 33. Write a quadratic function in vertex form that has a verte through the point (3,10) (3,10) .
  1. Vertex Form Equation: Vertex form of a quadratic function is y=a(x−h)2+ky = a(x - h)^2 + k, where (h,k)(h,k) is the vertex.
  2. Identifying Vertex: Given vertex is (3,10)(3,10), so h=3h = 3 and k=10k = 10.
  3. Substitute Values: Substitute h=3h = 3 and k=10k = 10 into the vertex form equation: y=a(x−3)2+10y = a(x - 3)^2 + 10.
  4. Determining 'a': We don't have another point to find the value of 'a', so the equation remains y=a(x−3)2+10y = a(x - 3)^2 + 10.
  5. Final Answer: Since we can't determine aa without additional information, the equation y=a(x−3)2+10y = a(x - 3)^2 + 10 is the final answer.

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