Solve the following quadratic function to find the x-intercepts: f(x) = x² + 12x + 27 x = 4 and -3 x = 9 and 3 x = -12 and 27 x = -4 and 3
Solve the following quadratic function to find the x-intercepts: f(x) = x² + 12x + 27 x = 4 and -3 x = 9 and 3 x = -12 and 27 x = -4 and 3
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
Related questions
Question
![**Problem:**
Solve the following quadratic function to find the x-intercepts:
\[ f(x) = x^2 + 12x + 27 \]
**Options:**
- ○ \( x = 4 \) and \(-3\)
- ○ \( x = 9 \) and \( 3 \)
- ○ \( x = -12 \) and \( 27 \)
- ○ \( x = -4 \) and \( 3 \)
**Solution Explanation:**
To find the x-intercepts of the quadratic function \( f(x) = x^2 + 12x + 27 \), set the function equal to zero and solve for \( x \):
\[ x^2 + 12x + 27 = 0 \]
Use the quadratic formula:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
where \( a = 1 \), \( b = 12 \), and \( c = 27 \). Calculate the values inside the square root (the discriminant):
\[ b^2 - 4ac = 12^2 - 4(1)(27) = 144 - 108 = 36 \]
Thus,
\[ x = \frac{-12 \pm \sqrt{36}}{2} \]
\[ x = \frac{-12 \pm 6}{2} \]
This yields two solutions:
\[ x = \frac{-12 + 6}{2} = -3 \]
\[ x = \frac{-12 - 6}{2} = -9 \]
So, the correct option is not listed in the original choices provided. The correct x-intercepts are \( x = -3 \) and \( x = -9 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2e1cb03f-91d2-4991-91c8-37c8965f1bd7%2Fbf460132-a0f1-4564-81ce-90421ebd2a55%2F6kwlzjs_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem:**
Solve the following quadratic function to find the x-intercepts:
\[ f(x) = x^2 + 12x + 27 \]
**Options:**
- ○ \( x = 4 \) and \(-3\)
- ○ \( x = 9 \) and \( 3 \)
- ○ \( x = -12 \) and \( 27 \)
- ○ \( x = -4 \) and \( 3 \)
**Solution Explanation:**
To find the x-intercepts of the quadratic function \( f(x) = x^2 + 12x + 27 \), set the function equal to zero and solve for \( x \):
\[ x^2 + 12x + 27 = 0 \]
Use the quadratic formula:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
where \( a = 1 \), \( b = 12 \), and \( c = 27 \). Calculate the values inside the square root (the discriminant):
\[ b^2 - 4ac = 12^2 - 4(1)(27) = 144 - 108 = 36 \]
Thus,
\[ x = \frac{-12 \pm \sqrt{36}}{2} \]
\[ x = \frac{-12 \pm 6}{2} \]
This yields two solutions:
\[ x = \frac{-12 + 6}{2} = -3 \]
\[ x = \frac{-12 - 6}{2} = -9 \]
So, the correct option is not listed in the original choices provided. The correct x-intercepts are \( x = -3 \) and \( x = -9 \).
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