Find the x-intercepts, if any. Express the intercept(s) as ordered pair(s) of k(x)=x^2+5x+4

To find the \( x \)-intercepts of the function \( k(x) = x^2 + 5x + 4 \), we need to solve for \( x \) when \( k(x) = 0 \). The \( x \)-intercepts occur where the graph of the function crosses the \( x \)-axis, meaning \( y = 0 \).

So, we set the equation to zero and solve for \( x \):

\[
x^2 + 5x + 4 = 0
\]

This is a quadratic equation, and we can solve it by factoring.

1. We look for two numbers that multiply to \( 4 \) (the constant term) and add to \( 5 \) (the coefficient of \( x \)).

These numbers are \( 4 \) and \( 1 \).

2. We can factor the quadratic as:

\[
(x + 4)(x + 1) = 0
\]

3. Now, we set each factor equal to zero and solve for \( x \):

\[
x + 4 = 0 \quad \text{or} \quad x + 1 = 0
\]

\[
x = -4 \quad \text{or} \quad x = -1
\]

So, the \( x \)-intercepts are at \( x = -4 \) and \( x = -1 \).

These intercepts can be expressed as the ordered pairs:

\[
(-4, 0) \quad \text{and} \quad (-1, 0)
\]

**Summary:**

The \( x \)-intercepts of the function \( k(x) = x^2 + 5x + 4 \) are \( (-4, 0) \) and \( (-1, 0) \).

Would you like more details on any part of the solution?

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Here are some related questions you might find helpful:

1. How do you find the vertex of the quadratic function \( k(x) = x^2 + 5x + 4 \)?
2. What is the axis of symmetry for the quadratic function \( k(x) = x^2 + 5x + 4 \)?
3. Can you express the function \( k(x) = x^2 + 5x + 4 \) in vertex form?
4. What is the y-intercept of the function \( k(x) = x^2 + 5x + 4 \)?
5. How do you graph the function \( k(x) = x^2 + 5x + 4 \)?
6. What are the roots of the equation \( k(x) = 0 \) using the quadratic formula?
7. How does completing the square help in finding the x-intercepts of \( k(x) = x^2 + 5x + 4 \)?
8. What is the discriminant of the quadratic equation \( k(x) = 0 \), and what does it tell us about the roots?

**Tip:** When factoring a quadratic, always check that the factors multiply to give the original quadratic equation, confirming the solution.

Learn how to find the x-intercepts of the quadratic function k(x) = x^2 + 5x + 4 using factoring. Detailed step-by-step solution provided. Suitable for students in Grades 7-9.

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