The graph of function g is a parabola with the vertex located at (5, 9). The parabo also passes through the point (3, 1). Write an equation in vertex form for this function. a = Equation:
The graph of function g is a parabola with the vertex located at (5, 9). The parabo also passes through the point (3, 1). Write an equation in vertex form for this function. a = Equation:
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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![**Problem 5:**
The graph of function \( g \) is a parabola with the vertex located at \( (5, 9) \). The parabola also passes through the point \( (3, 1) \). Write an equation in vertex form for this function.
Find the value of \( a \):
\[ a = \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\ \ \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\ ]\]
Write the equation in vertex form:
\[ \text{Equation:} \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\ \ \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\ \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\ ]\]
---
**Explanation:**
This problem involves finding the vertex form of the equation of a parabola given the vertex and another point through which the parabola passes.
1. First, recognize that the vertex form of a parabola's equation is given by:
\[ g(x) = a(x-h)^2 + k, \]
where \( (h, k) \) is the vertex of the parabola.
2. Given the vertex \((5, 9)\), we substitute \( h = 5 \) and \( k = 9 \) into the vertex form equation:
\[ g(x) = a(x-5)^2 + 9. \]
3. To find the value of \( a \), we use the given point \((3, 1)\). Substitute \( x = 3 \) and \( g(x) = 1 \) into the equation and solve for \( a \):
\[ 1 = a(3-5)^2 + 9. \]
4. Simplify](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9db37ba3-74ae-4145-b91c-cdd0f7d7a19a%2F6e4d33cd-8f90-47ed-a9dd-7024d3fe2f85%2Fz26j3wk_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem 5:**
The graph of function \( g \) is a parabola with the vertex located at \( (5, 9) \). The parabola also passes through the point \( (3, 1) \). Write an equation in vertex form for this function.
Find the value of \( a \):
\[ a = \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\ \ \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\ ]\]
Write the equation in vertex form:
\[ \text{Equation:} \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\ \ \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\ \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\ ]\]
---
**Explanation:**
This problem involves finding the vertex form of the equation of a parabola given the vertex and another point through which the parabola passes.
1. First, recognize that the vertex form of a parabola's equation is given by:
\[ g(x) = a(x-h)^2 + k, \]
where \( (h, k) \) is the vertex of the parabola.
2. Given the vertex \((5, 9)\), we substitute \( h = 5 \) and \( k = 9 \) into the vertex form equation:
\[ g(x) = a(x-5)^2 + 9. \]
3. To find the value of \( a \), we use the given point \((3, 1)\). Substitute \( x = 3 \) and \( g(x) = 1 \) into the equation and solve for \( a \):
\[ 1 = a(3-5)^2 + 9. \]
4. Simplify
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