Question
What are the x-intercepts of the function?
y = x^2 + 6x + 8
y = x^2 + 6x + 8
Answers
Answered by
GPT-4o mini
To find the x-intercepts of the function \( y = x^2 + 6x + 8 \), we need to set \( y \) to zero and solve for \( x \):
\[
0 = x^2 + 6x + 8
\]
Now, we can factor the quadratic equation. We want two numbers that multiply to \( 8 \) (the constant term) and add up to \( 6 \) (the coefficient of \( x \)). The numbers \( 2 \) and \( 4 \) satisfy these conditions:
\[
0 = (x + 2)(x + 4)
\]
Now, we set each factor equal to zero:
1. \( x + 2 = 0 \)
\[
x = -2
\]
2. \( x + 4 = 0 \)
\[
x = -4
\]
Therefore, the x-intercepts of the function \( y = x^2 + 6x + 8 \) are:
\[
x = -2 \quad \text{and} \quad x = -4
\]
In coordinate form, the x-intercepts are:
\[
(-2, 0) \quad \text{and} \quad (-4, 0)
\]
\[
0 = x^2 + 6x + 8
\]
Now, we can factor the quadratic equation. We want two numbers that multiply to \( 8 \) (the constant term) and add up to \( 6 \) (the coefficient of \( x \)). The numbers \( 2 \) and \( 4 \) satisfy these conditions:
\[
0 = (x + 2)(x + 4)
\]
Now, we set each factor equal to zero:
1. \( x + 2 = 0 \)
\[
x = -2
\]
2. \( x + 4 = 0 \)
\[
x = -4
\]
Therefore, the x-intercepts of the function \( y = x^2 + 6x + 8 \) are:
\[
x = -2 \quad \text{and} \quad x = -4
\]
In coordinate form, the x-intercepts are:
\[
(-2, 0) \quad \text{and} \quad (-4, 0)
\]