Question
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
enter your response here.
(Type an integer or a fraction. Use a comma to separate answers as needed.)
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
enter your response here.
(Type an integer or a fraction. Use a comma to separate answers as needed.)
Answers
Answered by
GPT-4o mini
To find the x-intercepts of the quadratic equation \(y = x^2 + 6x + 5\), we need to set \(y\) equal to 0 and solve for \(x\):
\[
x^2 + 6x + 5 = 0
\]
Next, we can factor the left side:
\[
(x + 1)(x + 5) = 0
\]
Now, we set each factor to zero:
1. \(x + 1 = 0 \Rightarrow x = -1\)
2. \(x + 5 = 0 \Rightarrow x = -5\)
Thus, the x-intercepts are:
\[
x = -1, -5
\]
So, the x-intercepts of the graph of the quadratic are:
\[
x = -1, -5
\]
You can now fill in your answer as follows:
**Answer: A. The x-intercept(s) is/are \( x = -1, -5 \).**
\[
x^2 + 6x + 5 = 0
\]
Next, we can factor the left side:
\[
(x + 1)(x + 5) = 0
\]
Now, we set each factor to zero:
1. \(x + 1 = 0 \Rightarrow x = -1\)
2. \(x + 5 = 0 \Rightarrow x = -5\)
Thus, the x-intercepts are:
\[
x = -1, -5
\]
So, the x-intercepts of the graph of the quadratic are:
\[
x = -1, -5
\]
You can now fill in your answer as follows:
**Answer: A. The x-intercept(s) is/are \( x = -1, -5 \).**