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Subjects
Class 11MathematicsRelations and FunctionsGraphs of standard functionsMedium
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For real values of \(x\), what is the maximum value of the function \(f(x)=-(x+2)^2+5\)?

Answer and explanation

Correct answer: 5

Since \((x+2)^2\ge 0\), we have \(-(x+2)^2\le 0\), so \(f(x)=-(x+2)^2+5\le 5\). Equality occurs when \(x=-2\), hence the maximum value is 5. Note that \(-2\) is the x-coordinate of the vertex, not the maximum value of the function. Exam tip: for a downward-opening parabola, the y-coordinate of the vertex gives the maximum value.

Related tags

Standard-FunctionsQuadratic-GraphMaximum-ValueGraphs Of Standard FunctionsRelations And FunctionsMathematicsClass 11 Mcq
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10 more MCQs
  1. 1If f(x)=x^2 and A={1,2,3} is the domain of f, which of the following is the graph of f on A?
  2. 2Which relation represents the graph of the rule \(y=x+2\) for the inputs in the set \(A=\{1,3\}\)?
  3. 3If f(x)=3x and its domain is A={0,1,2}, which of the following is the graph of the function defined on A?
  4. 4If \(f:\{1,2,3,4\}\to\{1,2,3,4\}\) and \(f(x)=5-x\), which of the following is the graph of \(f\)?
  5. 5What is the usual graph of the function (f(x)=x)?
  6. 6What is the graph of (f(x)=c), where (c) is a constant?
  7. 7Which shape represents the graph of (f(x)=x^2)?
  8. 8In which direction does the graph of (f(x)=-x^2) open?
  9. 9The graph of (f(x)=|x|) is symmetric about which axis?
  10. 10Through which point does the graph of f(x)=x³ pass?
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