Question
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Part 1
Determine the x-intercepts of the graph of the quadratic. Then match the function with its graph. Each graph is shown in a left bracket negative 10 comma 10 comma 1 right bracket by left bracket negative 10 comma 10 comma 1 right bracket viewing rectangle.
y equals x squared plus 6 x plus 5
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Part 1
Select the correct choice below and fill in any answer boxes within your choice.
A.
The x-intercept(s) is/are xequals
negative 1 comma negative 5.
(Type an integer or a fraction. Use a comma to separate answers as needed.)
Your answer is correct.B.
There are no x-intercepts.
Part 2
Choose the correct graph below.
A.
A coordinate system has a horizontal axis labeled from negative 10 to 10 in increments of 1 and a vertical axis labeled from negative 10 to 10 in increments of 1. A parabola that opens upward has vertex (negative 3, negative 4) and passes through the points (negative 5, 0) and (negative 1, 0). All coordinates are approximate.
B.
A coordinate system has a horizontal x-axis labeled from negative 10 to 10 in increments of 1 and a vertical y-axis labeled from negative 10 to 10 in increments of 1. A parabola that opens upward has vertex (2, negative 9) and passes through the points (5, 0) and (negative 1, 0). All coordinates are approximate.
C.
A coordinate system has a horizontal axis labeled from negative 10 to 10 in increments of 1 and a vertical axis labeled from negative 10 to 10 in increments of 1. A parabola that opens upward has vertex (3, negative 4) and passes through the points (5, 0) and (1, 0). All coordinates are approximate.
D.
Part 1
Determine the x-intercepts of the graph of the quadratic. Then match the function with its graph. Each graph is shown in a left bracket negative 10 comma 10 comma 1 right bracket by left bracket negative 10 comma 10 comma 1 right bracket viewing rectangle.
y equals x squared plus 6 x plus 5
Question content area bottom
Part 1
Select the correct choice below and fill in any answer boxes within your choice.
A.
The x-intercept(s) is/are xequals
negative 1 comma negative 5.
(Type an integer or a fraction. Use a comma to separate answers as needed.)
Your answer is correct.B.
There are no x-intercepts.
Part 2
Choose the correct graph below.
A.
A coordinate system has a horizontal axis labeled from negative 10 to 10 in increments of 1 and a vertical axis labeled from negative 10 to 10 in increments of 1. A parabola that opens upward has vertex (negative 3, negative 4) and passes through the points (negative 5, 0) and (negative 1, 0). All coordinates are approximate.
B.
A coordinate system has a horizontal x-axis labeled from negative 10 to 10 in increments of 1 and a vertical y-axis labeled from negative 10 to 10 in increments of 1. A parabola that opens upward has vertex (2, negative 9) and passes through the points (5, 0) and (negative 1, 0). All coordinates are approximate.
C.
A coordinate system has a horizontal axis labeled from negative 10 to 10 in increments of 1 and a vertical axis labeled from negative 10 to 10 in increments of 1. A parabola that opens upward has vertex (3, negative 4) and passes through the points (5, 0) and (1, 0). All coordinates are approximate.
D.
Answers
Answered by
GPT-4o mini
To find the x-intercepts of the quadratic function \( y = x^2 + 6x + 5 \), we will set \( y \) to zero and solve for \( x \).
1. Set the equation to zero:
\[
0 = x^2 + 6x + 5
\]
2. Factor the quadratic:
\[
0 = (x + 1)(x + 5)
\]
3. Set each factor to zero:
\[
x + 1 = 0 \quad \Rightarrow \quad x = -1
\]
\[
x + 5 = 0 \quad \Rightarrow \quad x = -5
\]
Thus, the x-intercepts are \( x = -1 \) and \( x = -5 \). Therefore, the answer to Part 1 is:
- A. The x-intercept(s) is/are \( x = -1, -5 \).
### Part 2: Choose the correct graph
Now we need to match these x-intercepts with the appropriate graph. The function has x-intercepts at \( (-1, 0) \) and \( (-5, 0) \).
- Looking at Graph A:
- It has a parabola that passes through the points \( (-5, 0) \) and \( (-1, 0) \), which matches the x-intercepts we calculated.
- Graph B and C do not intersect at \( -1 \) and \( -5 \).
- Graph D is not provided in detail in this format.
Hence, the correct graph is:
- **A.** The graph of the parabola that opens upward, with x-intercepts at the points \( (-5, 0) \) and \( (-1, 0) \).
So the answers are:
- Part 1: \( x = -1, -5 \)
- Part 2: Graph A.
1. Set the equation to zero:
\[
0 = x^2 + 6x + 5
\]
2. Factor the quadratic:
\[
0 = (x + 1)(x + 5)
\]
3. Set each factor to zero:
\[
x + 1 = 0 \quad \Rightarrow \quad x = -1
\]
\[
x + 5 = 0 \quad \Rightarrow \quad x = -5
\]
Thus, the x-intercepts are \( x = -1 \) and \( x = -5 \). Therefore, the answer to Part 1 is:
- A. The x-intercept(s) is/are \( x = -1, -5 \).
### Part 2: Choose the correct graph
Now we need to match these x-intercepts with the appropriate graph. The function has x-intercepts at \( (-1, 0) \) and \( (-5, 0) \).
- Looking at Graph A:
- It has a parabola that passes through the points \( (-5, 0) \) and \( (-1, 0) \), which matches the x-intercepts we calculated.
- Graph B and C do not intersect at \( -1 \) and \( -5 \).
- Graph D is not provided in detail in this format.
Hence, the correct graph is:
- **A.** The graph of the parabola that opens upward, with x-intercepts at the points \( (-5, 0) \) and \( (-1, 0) \).
So the answers are:
- Part 1: \( x = -1, -5 \)
- Part 2: Graph A.