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Use the quadratic function f(x)=14x2+4x+11f(x)=\frac{1}{4}x^{2}+4x+11 to answer the following questions. Use the vertex formula to determine the vertex. \newlineThe vertex is ◻.\newline (Type an ordered pair. Simplify your answer.)

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One-step inequalities: word problemsright chevron icon

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Q. Use the quadratic function f(x)=14x2+4x+11f(x)=\frac{1}{4}x^{2}+4x+11 to answer the following questions. Use the vertex formula to determine the vertex. \newlineThe vertex is ◻.\newline (Type an ordered pair. Simplify your answer.)
  1. Identify Formula: Identify the formula for the vertex of a quadratic function in the form f(x)=ax2+bx+cf(x) = ax^2 + bx + c. The vertex xx-coordinate is given by x=−b2ax = -\frac{b}{2a}.
  2. Substitute Coefficients: Substitute the coefficients a=14a = \frac{1}{4} and b=4b = 4 into the vertex formula. Calculate x=−42⋅(14)=−40.5=−8x = -\frac{4}{2 \cdot (\frac{1}{4})} = -\frac{4}{0.5} = -8.
  3. Calculate Y-coordinate: Substitute x=−8x = -8 into the function to find the y-coordinate of the vertex. Calculate f(−8)=(14)(−8)2+4(−8)+11=16−32+11=−5f(-8) = (\frac{1}{4})(-8)^2 + 4(-8) + 11 = 16 - 32 + 11 = -5.
  4. Combine Coordinates: Combine the coordinates to form the vertex. The vertex is (−8,−5)(-8, -5).

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