5. Determine the equation of the graph below. Choose the correct equation. 5- a) y = (x– 2)² + 3 b) y = (x - 2)2 – 3 c) y = (x + 2)² + 3 d) y = (x + 2)? – 3 2 10 -2 1 -1- 5. 6. -3- -4- -5- -6+
5. Determine the equation of the graph below. Choose the correct equation. 5- a) y = (x– 2)² + 3 b) y = (x - 2)2 – 3 c) y = (x + 2)² + 3 d) y = (x + 2)? – 3 2 10 -2 1 -1- 5. 6. -3- -4- -5- -6+
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter9: Quadratic Functions And Equations
Section9.7: Solving Systems Of Linear And Quadratic Equations
Problem 14PPS
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![### Quadratic Function Analysis
**Problem Statement:**
5. Determine the equation of the graph below. Choose the correct equation.
**Options:**
a) \( y = (x - 2)^2 + 3 \)
b) \( y = (x - 2)^2 - 3 \)
c) \( y = (x + 2)^2 + 3 \)
d) \( y = (x + 2)^2 - 3 \)
**Graph:**
The graph depicts a parabola opening upwards with its vertex appearing at the point \((-2, -3)\). The x-axis ranges from \(-6\) to \(6\), and the y-axis ranges from \(-6\) to \(6\).
### Explanation of the Graph:
- The parabola is a quadratic function in the standard form \( y = a(x - h)^2 + k \).
- The vertex form of a parabola is given by \( y = a(x - h)^2 + k \), where \( (h, k) \) is the vertex of the parabola.
- Based on the graph, the vertex of the parabola is \((-2, -3)\).
Considering the form of the vertex \( (h, k) \):
- The x-coordinate \( h \) is \(-2\),
- The y-coordinate \( k \) is \(-3\).
Thus, the equation of the parabola should be:
\[ y = a(x + 2)^2 - 3 \]
Since the parabola opens upwards, the coefficient \( a \) is positive and specifically it is 1 here. Hence, the correct equation matching the vertex of \((-2, -3)\) is:
**Answer:**
\[ \boxed{d \: y = (x + 2)^2 - 3} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fba45ef30-7373-40a6-93b1-6069d924f96b%2Fcb9faad9-4870-4aa5-b144-c837d71da8c0%2Ftjcgr6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Quadratic Function Analysis
**Problem Statement:**
5. Determine the equation of the graph below. Choose the correct equation.
**Options:**
a) \( y = (x - 2)^2 + 3 \)
b) \( y = (x - 2)^2 - 3 \)
c) \( y = (x + 2)^2 + 3 \)
d) \( y = (x + 2)^2 - 3 \)
**Graph:**
The graph depicts a parabola opening upwards with its vertex appearing at the point \((-2, -3)\). The x-axis ranges from \(-6\) to \(6\), and the y-axis ranges from \(-6\) to \(6\).
### Explanation of the Graph:
- The parabola is a quadratic function in the standard form \( y = a(x - h)^2 + k \).
- The vertex form of a parabola is given by \( y = a(x - h)^2 + k \), where \( (h, k) \) is the vertex of the parabola.
- Based on the graph, the vertex of the parabola is \((-2, -3)\).
Considering the form of the vertex \( (h, k) \):
- The x-coordinate \( h \) is \(-2\),
- The y-coordinate \( k \) is \(-3\).
Thus, the equation of the parabola should be:
\[ y = a(x + 2)^2 - 3 \]
Since the parabola opens upwards, the coefficient \( a \) is positive and specifically it is 1 here. Hence, the correct equation matching the vertex of \((-2, -3)\) is:
**Answer:**
\[ \boxed{d \: y = (x + 2)^2 - 3} \]
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