To match the equations on the left with their equivalent forms on the right, we first need to check the provided equations and factor or expand them as necessary.
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y = x^2 - 1x - 20
- This equation can be factored. We need two numbers that multiply to -20 and add to -1. Those numbers are 4 and -5.
- So, \(y = (x - 5)(x + 4)\).
- Matches with C) y = (x + 4) (x - 5).
-
y = (x + 8)(x + 11)
- We can expand this:
- \(y = x^2 + 11x + 8x + 88 = x^2 + 19x + 88\).
- Matches with D) y = x^2 + 19x + 88.
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y = x^2 - 6x + 16
- We can complete the square or analyze the quadratic.
- Rewrite: \(y = (x - 3)^2 + 7\).
- This is because \((x - 3)^2\) expands to \(x^2 - 6x + 9\), and adding 7 gives the correct number.
- Matches with B) y = (x - 3)^2 + 7.
-
y = (x + 4)^2 - 5
- Rewrite by expanding:
- \(y = (x^2 + 8x + 16 - 5) = x^2 + 8x + 11\).
- Matches with A) y = x^2 + 8x + 11.
So, the final match is:
- \(y = x^2 - 1x - 20\) → C) y = (x + 4) (x - 5)
- \(y = (x + 8)(x + 11)\) → D) y = x^2 + 19x + 88
- \(y = x^2 - 6x + 16\) → B) y = (x - 3)^2 + 7
- \(y = (x + 4)^2 - 5\) → A) y = x^2 + 8x + 11