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NY Regents Algebra II Quadratic Functions — practice questions

Explore 4 free Quadratic Functions questions in NY Regents Algebra II Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Quadratic Functions questions and exercises with answers

Showing questions 1–4 of 4.

For f(x) = a(x - h) squared + k, what does a size of a above 1 do to the graph?Read the answer and worked solution →For f(x) = 2x squared - 12x + 5, what is the equation of the axis of symmetry?Read the answer and worked solution →A quadratic is written as f(x) = -3(x - 4) squared + 7. Where is its vertex?Read the answer and worked solution →Merge a culture through four hoursRead the answer and worked solution →

Worked practice questions

For f(x) = a(x - h) squared + k, what does a size of a above 1 do to the graph?

  1. The graph becomes wider
  2. The graph shifts upward
  3. The graph becomes narrower
  4. The graph shifts sideways
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Correct answer: C. The graph becomes narrower

1. The number a in front of the squared bracket controls a vertical stretch. 2. A size above 1 pulls every point further from the horizontal axis. 3. So the parabola looks narrower, while a size below 1 makes it look wider. _Source: OpenStax Precalculus (CC BY 4.0), section 3.2 Quadratic Functions_

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For f(x) = 2x squared - 12x + 5, what is the equation of the axis of symmetry?

  1. x = 3
  2. x = 6
  3. x = -3
  4. x = 12
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Correct answer: A. x = 3

1. The axis of symmetry of a quadratic in general form is the vertical line x equal to negative b over 2a. 2. Here a is 2 and b is negative 12. 3. So x equals 12 divided by 4, which is 3. 4. Forgetting to divide by 2a would give the wrong value 6. _Source: OpenStax Precalculus (CC BY 4.0), section 3.2 Quadratic Functions_

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A quadratic is written as f(x) = -3(x - 4) squared + 7. Where is its vertex?

  1. At (-4, 7)
  2. At (4, 7)
  3. At (4, -7)
  4. At (7, 4)
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Correct answer: B. At (4, 7)

1. Standard form for a quadratic is a times (x minus h) squared plus k, and (h, k) is the vertex. 2. Matching gives h equal to 4 and k equal to 7. 3. So the vertex sits at (4, 7). 4. Reading the sign inside the bracket as the sign of h would wrongly give negative 4. _Source: OpenStax Precalculus (CC BY 4.0), section 3.2 Quadratic Functions_

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More Mathematics topics

Complex NumbersExponential and Logarithmic ModelsGraphs of Polynomial FunctionsPower and Polynomial FunctionsRational FunctionsZeros of Polynomial FunctionsProperties of LogarithmsDividing Polynomials