Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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![**Quadratic Equation Standard Form Conversion**
*Objective*: Convert the given quadratic equation from its general form to standard form.
**Problem Statement:**
Put the equation that is in general form: \( y = x^2 + 12x + 32 \)
into standard form: \( y = (x - h)^2 + k \).
**Answer:** \( y = \) [ANSWER BOX]
To express the quadratic equation in standard form, follow these steps:
1. **Identify the given quadratic equation in general form**:
\( y = x^2 + 12x + 32 \).
2. **Complete the square** to rewrite the quadratic equation in the form \( y = (x - h)^2 + k \):
- Begin by focusing on the quadratic and linear terms:
\( x^2 + 12x \).
- To complete the square, add and subtract the square of half the coefficient of \( x \) inside the equation:
\( x^2 + 12x \rightarrow x^2 + 12x + 36 - 36 \).
- Rewrite the equation with the completed square term:
\( y = (x^2 + 12x + 36) - 36 + 32 \).
- Simplify the equation:
\( y = (x + 6)^2 - 4 \).
Thus, the equivalent equation in standard form is:
\( y = (x + 6)^2 - 4 \).
Feel free to use the provided box to input the standard form of the given quadratic equation.](https://content.bartleby.com/qna-images/question/8b3342fe-b335-4689-a0aa-7d956754a511/cbb7c0ec-3cd4-4f8c-a087-127fd4f22a9d/xmaouh9_processed.png)
Transcribed Image Text:**Quadratic Equation Standard Form Conversion**
*Objective*: Convert the given quadratic equation from its general form to standard form.
**Problem Statement:**
Put the equation that is in general form: \( y = x^2 + 12x + 32 \)
into standard form: \( y = (x - h)^2 + k \).
**Answer:** \( y = \) [ANSWER BOX]
To express the quadratic equation in standard form, follow these steps:
1. **Identify the given quadratic equation in general form**:
\( y = x^2 + 12x + 32 \).
2. **Complete the square** to rewrite the quadratic equation in the form \( y = (x - h)^2 + k \):
- Begin by focusing on the quadratic and linear terms:
\( x^2 + 12x \).
- To complete the square, add and subtract the square of half the coefficient of \( x \) inside the equation:
\( x^2 + 12x \rightarrow x^2 + 12x + 36 - 36 \).
- Rewrite the equation with the completed square term:
\( y = (x^2 + 12x + 36) - 36 + 32 \).
- Simplify the equation:
\( y = (x + 6)^2 - 4 \).
Thus, the equivalent equation in standard form is:
\( y = (x + 6)^2 - 4 \).
Feel free to use the provided box to input the standard form of the given quadratic equation.
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