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HiSET The Quadratic Formula — practice questions

Explore 7 free The Quadratic Formula questions in HiSET Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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The Quadratic Formula questions and exercises with answers

Showing questions 1–7 of 7.

What is the standard form of a quadratic equation?Read the answer and worked solution →What is the expression b squared minus 4ac called?Read the answer and worked solution →The discriminant of a quadratic equation is positive. How many solutions does it have?Read the answer and worked solution →A quadratic in standard form is a perfect square trinomial set equal to 0. How many solutions has it?Read the answer and worked solution →Use the quadratic formula on 2x squared plus 5x minus 3 = 0. What are the solutions?Read the answer and worked solution →How many solutions does 3x squared plus 4x plus 5 = 0 have, and of what type?Read the answer and worked solution →Line up three discriminants of one signRead the answer and worked solution →

Worked practice questions

What is the standard form of a quadratic equation?

  1. ax cubed + bx + c = 0
  2. ax + bx squared = c
  3. ax squared + bx = cx
  4. ax squared + bx + c = 0
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Correct answer: D. ax squared + bx + c = 0

1. A quadratic equation has a term in which the variable is raised to the second power. 2. In standard form every term is collected on one side and the other side is 0. 3. That gives ax squared plus bx plus c equal to 0, where a may not be 0. _Source: OpenStax Intermediate Algebra (CC BY 4.0), section 9.3 Solve Quadratic Equations Using the Quadratic Formula_

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What is the expression b squared minus 4ac called?

  1. The coefficient
  2. The discriminant
  3. The determinant
  4. The remainder
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Correct answer: B. The discriminant

1. The quadratic formula holds a square root, and b squared minus 4ac sits under it. 2. That expression is called the discriminant. 3. Its sign alone tells how many solutions there are and whether they are real or complex. _Source: OpenStax Intermediate Algebra (CC BY 4.0), section 9.3 Solve Quadratic Equations Using the Quadratic Formula_

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The discriminant of a quadratic equation is positive. How many solutions does it have?

  1. One real solution
  2. Two complex solutions
  3. Two real solutions
  4. Four real solutions
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Correct answer: C. Two real solutions

1. The discriminant sits under the square root in the quadratic formula. 2. A positive value has two real square roots, one positive and one negative. 3. The formula then produces two different real solutions. 4. A discriminant of 0 would give only one solution, since adding and subtracting 0 gives the same value. _Source: OpenStax Intermediate Algebra (CC BY 4.0), section 9.3 Solve Quadratic Equations Using the Quadratic Formula_

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More Mathematics topics

Graphing Quadratic FunctionsLogarithmic FunctionsApplications of Quadratic EquationsExponential and Logarithmic EquationsQuadratic InequalitiesSquare Root PropertyEquations in Quadratic FormExponential Functions