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Which of the following quadratic equations has a maximum value?

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Question: Which of the following quadratic equations has a maximum value?

Options:

  1. x² + 4x + 4 = 0
  2. x² - 2x + 1 = 0
  3. x² - 3x + 2 = 0
  4. x² + 2x - 8 = 0

Correct Answer: x² + 4x + 4 = 0

Solution: 

A quadratic equation has a maximum value when the coefficient of x² is negative. Here, all options have a positive coefficient, but the first option can be rewritten to show its vertex form.

Which of the following quadratic equations has a maximum value?

Practice Questions

Q1
Which of the following quadratic equations has a maximum value?
  1. x² + 4x + 4 = 0
  2. x² - 2x + 1 = 0
  3. x² - 3x + 2 = 0
  4. x² + 2x - 8 = 0

Questions & Step-by-Step Solutions

Which of the following quadratic equations has a maximum value?
  • Step 1: Understand what a quadratic equation is. A quadratic equation is in the form of ax² + bx + c, where a, b, and c are numbers.
  • Step 2: Identify the coefficient of x², which is 'a'. This coefficient determines if the quadratic opens upwards or downwards.
  • Step 3: Remember that if 'a' is positive (greater than 0), the quadratic opens upwards and has a minimum value. If 'a' is negative (less than 0), the quadratic opens downwards and has a maximum value.
  • Step 4: Look at the options given in the question. Check the coefficient of x² in each option.
  • Step 5: If all options have a positive coefficient for x², then none of them can have a maximum value.
  • Step 6: If one of the options can be rewritten to show its vertex form, check if it has a negative coefficient when rewritten.
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