Put the equation that is in general form: y = x² + 12x + 32 into standard form: y = (x - h)² + k: Answer: y =
Put the equation that is in general form: y = x² + 12x + 32 into standard form: y = (x - h)² + k: Answer: y =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![**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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8b3342fe-b335-4689-a0aa-7d956754a511%2Fcbb7c0ec-3cd4-4f8c-a087-127fd4f22a9d%2Fxmaouh9_processed.png&w=3840&q=75)
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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