How do you write #5n^2+19n-68=-2# into vertex form?
Take the constant out of the working left side for the time being.
Finish the square.
To finish the vertex form, move the constant back to the left:
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To write the quadratic equation (5n^2 + 19n - 68 = -2) into vertex form, follow these steps:
- Rewrite the equation in standard form: (5n^2 + 19n - 66 = 0).
- Factor out the leading coefficient (a): (5(n^2 + \frac{19}{5}n) - 66 = 0).
- Complete the square inside the parentheses: (5(n^2 + \frac{19}{5}n + (\frac{19}{10})^2) - 66 - 5(\frac{19}{10})^2 = 0).
- Simplify inside the parentheses: (5(n^2 + \frac{19}{5}n + \frac{361}{100}) - 66 - \frac{361}{4} = 0).
- Rewrite the constant term: (5(n^2 + \frac{19}{5}n + \frac{361}{100}) - \frac{2644}{25} = 0).
- Rewrite the constant term as a perfect square: (5(n + \frac{19}{10})^2 - \frac{2644}{25} = 0).
- Move the constant term to the other side: (5(n + \frac{19}{10})^2 = \frac{2644}{25}).
- Divide both sides by the leading coefficient (a): (n + \frac{19}{10})^2 = \frac{2644}{125}).
- The vertex form is (n + \frac{19}{10})^2 = \frac{2644}{125}).
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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