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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Question
![**Problem Statement:**
Find \( b \) and \( c \) so that \( y = 10x^2 + bx + c \) has vertex \( (-8, 0) \).
**Solution Inputs:**
- \( b = \) [Input box]
- \( c = \) [Input box]
**Explanation:**
To solve this problem, we need to use the fact that the vertex form of a quadratic equation is \( y = a(x-h)^2 + k \), where \((h, k)\) is the vertex of the parabola.
Given that the vertex is \((-8, 0)\) and \( a = 10\), we can use the vertex formula to find the values of \( b \) and \( c \). The vertex form and standard form should equate for us to find these relations. The vertex’s x-coordinate gives the relation \( h = -\frac{b}{2a} \). Using these equations, we can find the constants \( b \) and \( c \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcf99ef9a-11bc-4c83-b49c-a6b52894d845%2F89791f23-6e4e-4d6b-9deb-efc3a39511c8%2Fq1no8b_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find \( b \) and \( c \) so that \( y = 10x^2 + bx + c \) has vertex \( (-8, 0) \).
**Solution Inputs:**
- \( b = \) [Input box]
- \( c = \) [Input box]
**Explanation:**
To solve this problem, we need to use the fact that the vertex form of a quadratic equation is \( y = a(x-h)^2 + k \), where \((h, k)\) is the vertex of the parabola.
Given that the vertex is \((-8, 0)\) and \( a = 10\), we can use the vertex formula to find the values of \( b \) and \( c \). The vertex form and standard form should equate for us to find these relations. The vertex’s x-coordinate gives the relation \( h = -\frac{b}{2a} \). Using these equations, we can find the constants \( b \) and \( c \).
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