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DIRECTIONS:

Determine whether the indicated ordered pair is a solution to the quadratic inequality y < x² + 4x - 5. Justify your answer.

  • Substitute the value of x and y to see if the pair is a solution to the quadratic inequality.

1.) A (-2, 5)

[tex]y \: < {x}^{2} + 4x - 5 \\ 5 < ( - 2 {)}^{2} + 4( - 2) - 5 \\ 5 < 4 - 8 - 5 \\ 5 < - 4 - 5 \\ 5 < - 9 [/tex]

  • Is 5 less than -9? No, 5 is greater than -9.
  • This is not a Solution.

2.) B (6, -2)

[tex]y < {x}^{2} + 4x - 5 \\ - 2 < (6 {)}^{2} + 4(6) - 5 \\ - 2 < 36 + 24 - 5 \\ - 2 < 60 - 5 \\ - 2 < 55[/tex]

  • Is -2 less than 55? Yes.
  • This is a Solution.

3.) C (-3, 2)

[tex]y < {x}^{2} + 4x - 5 \\ 2 < ( - 3 {)}^{2} + 4( - 3) - 5 \\ 2 < 9 - 12 - 5 \\ 2 < - 3 - 5 \\ 2 < - 8[/tex]

  • Is 2 less than -8? No, 2 is greater than -8.
  • This is not a Solution.

4.) D (1, -1)

[tex]y < {x}^{2} + 4 - 5 \\ - 1 < (1 {)}^{2} + 4(1) - 5 \\ - 1 < 1 + 4 - 5 \\ - 1 < 5 - 5 \\ - 1 < 0[/tex]

  • Is -1 less than 0? Yes, any negative integers are less than zero.
  • This is a Solution.

5.) E (2, -2)

[tex]y < {x}^{2} + 4x - 5 \\ - 2 < (2 {)}^{2} + 4(2) - 5 \\ - 2 < 4 + 8 - 5 \\ - 2 < 12 - 5 \\ - 2 < 7[/tex]

  • Is -2 less than 7? Yes.
  • This is a Solution.

ANSWERS:

1. Not a Solution

2. Solution

3. Not a Solution

4. Solution

5. Solution

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