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Y. 6 Write a quadratic function in verte abola is y=4x^(2)-12 x+13. Write the equati integers or simplified proper or improper fra

Y. 66 Write a quadratic function in verte\newlineabola is y=4x2−12x+13 y=4 x^{2}-12 x+13 . Write the equati\newlineintegers or simplified proper or improper fra

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Q. Y. 66 Write a quadratic function in verte\newlineabola is y=4x2−12x+13 y=4 x^{2}-12 x+13 . Write the equati\newlineintegers or simplified proper or improper fra
  1. Identify Quadratic Function: Identify the quadratic function. y=4x2−12x+13y = 4x^2 - 12x + 13
  2. Find Vertex Form: Find the vertex form of a quadratic function, which is y=a(x−h)2+ky = a(x - h)^2 + k.
  3. Calculate Vertex x-coordinate: Calculate the x-coordinate of the vertex hh using the formula h=−b2ah = -\frac{b}{2a}.\newlineFor the given function, a=4a = 4 and b=−12b = -12.\newlineh=−−122⋅4=128=1.5h = -\frac{-12}{2\cdot 4} = \frac{12}{8} = 1.5
  4. Calculate Vertex y-coordinate: Calculate the y-coordinate of the vertex kk by plugging hh into the original equation.\newlinek=4(1.5)2−12(1.5)+13k = 4(1.5)^2 - 12(1.5) + 13\newlinek=4(2.25)−18+13k = 4(2.25) - 18 + 13\newlinek=9−18+13k = 9 - 18 + 13\newlinek=4k = 4
  5. Write Quadratic Function in Vertex Form: Write the quadratic function in vertex form using the values of hh and kk.y=4(x−1.5)2+4y = 4(x - 1.5)^2 + 4

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