HiSET Applications of Quadratic Equations — practice questions

Explore 4 free Applications of Quadratic Equations questions in HiSET Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Applications of Quadratic Equations questions and exercises with answers

Showing questions 1–4 of 4.

If n is the first of two consecutive odd integers, how is the second written?Read the answer and worked solution →The product of two consecutive odd integers is 143. What is the larger positive integer?Read the answer and worked solution →Judge each claim about the two graphsRead the answer and worked solution →Type the exponent each logarithm hidesRead the answer and worked solution →

Worked practice questions

If n is the first of two consecutive odd integers, how is the second written?

As n plus 1
As n plus 2
As n plus 3
As 2 times n

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Correct answer: B. As n plus 2

1. Odd integers step up by 2 each time, just as even integers do. 2. So the integer after n in an odd run is n plus 2. 3. The one after that is n plus 4. 4. Writing n plus 1 would jump to the next integer of the opposite parity instead. _Source: OpenStax Intermediate Algebra (CC BY 4.0), section 9.5 Solve Applications of Quadratic Equations_

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The product of two consecutive odd integers is 143. What is the larger positive integer?

The integer 11
The integer 13
The integer 15
The integer 17

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Correct answer: B. The integer 13

1. Let n stand for the first odd integer, so the next one is n plus 2. 2. Their product is 143, giving n times the bracket (n plus 2) equal to 143. 3. Expanding gives n squared plus 2n equal to 143. 4. Writing that in standard form gives n squared plus 2n minus 143 equal to 0. 5. Factoring gives the brackets (n plus 13) and (n minus 11). 6. The positive solution is n equal to 11, so the pair is 11 and 13. 7. Checking, 11 times 13 is 143, so the larger integer is 13. 8. The integer 11 names the smaller member of the pair rather than the larger. 9. The integers 15 and 17 multiply to 255, which is far above 143. _Source: OpenStax Intermediate Algebra (CC BY 4.0), section 9.5 Solve Applications of Quadratic Equations_

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Judge each claim about the two graphs

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Questions

Statement is true
Yes
Statement
An exponential graph crosses the vertical axis at the point (0, 1).
Statement is true
No
Statement
An exponential graph dips below the horizontal axis for large inputs.
Statement is true
Yes
Statement
A logarithmic graph crosses the horizontal axis at the point (1, 0).
Statement is true
No
Statement
A logarithmic graph has a horizontal asymptote along the line y = 0.
Statement is true
Yes
Statement
The domain of a logarithmic function is every positive number.
Statement is true
No
Statement
The range of an exponential function is every real number.

Instructions

Tap true or false for each claim about exponential and logarithmic graphs.

_Source: OpenStax Intermediate Algebra (CC BY 4.0), section 10.3 Evaluate and Graph Logarithmic Functions_

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