Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![### Parabola Equation in Intercept Form
**Problem Statement:**
Write an equation in intercept form of the parabola that passes through the point \((-3, 35)\) and has \(x\)-intercepts \(-2\) and \(4\).
**Solution:**
We will write the equation of the parabola in intercept form, which is given by:
\[ y = a(x - p)(x - q) \]
Here, \(p\) and \(q\) are the \(x\)-intercepts, and \(a\) is a constant.
Given the \(x\)-intercepts \(-2\) and \(4\), we can substitute them into the equation:
\[ y = a(x + 2)(x - 4) \]
Next, we know the parabola passes through the point \((-3, 35)\). Substituting \((-3, 35)\) into the equation:
\[ 35 = a(-3 + 2)(-3 - 4) \]
\[ 35 = a(-1)(-7) \]
\[ 35 = 7a \]
\[ a = 5 \]
So, the equation of the parabola is:
\[ y = 5(x + 2)(x - 4) \]
### Final Answer:
\[ y = 5(x + 2)(x - 4) \]
This is the required equation in intercept form of the parabola that passes through the point \((-3, 35)\) and has \(x\)-intercepts \(-2\) and \(4\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2a18a320-2046-4089-b27e-0ca38db1d2b2%2F0046f531-bcd3-46db-9118-da9cc515b8c9%2Fpaijj7m.jpeg&w=3840&q=75)
Transcribed Image Text:### Parabola Equation in Intercept Form
**Problem Statement:**
Write an equation in intercept form of the parabola that passes through the point \((-3, 35)\) and has \(x\)-intercepts \(-2\) and \(4\).
**Solution:**
We will write the equation of the parabola in intercept form, which is given by:
\[ y = a(x - p)(x - q) \]
Here, \(p\) and \(q\) are the \(x\)-intercepts, and \(a\) is a constant.
Given the \(x\)-intercepts \(-2\) and \(4\), we can substitute them into the equation:
\[ y = a(x + 2)(x - 4) \]
Next, we know the parabola passes through the point \((-3, 35)\). Substituting \((-3, 35)\) into the equation:
\[ 35 = a(-3 + 2)(-3 - 4) \]
\[ 35 = a(-1)(-7) \]
\[ 35 = 7a \]
\[ a = 5 \]
So, the equation of the parabola is:
\[ y = 5(x + 2)(x - 4) \]
### Final Answer:
\[ y = 5(x + 2)(x - 4) \]
This is the required equation in intercept form of the parabola that passes through the point \((-3, 35)\) and has \(x\)-intercepts \(-2\) and \(4\).
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