k(x)=x2+5x+4k(x)=x2+5x+4

Find two points on the graph of the parabola other than the vertex and x-intercepts.

To find two points on the graph of the parabola defined by the function \( k(x) = x^2 + 5x + 4 \) other than the vertex and \( x \)-intercepts, we can choose any values of \( x \) that are different from the \( x \)-intercepts, \( x = -4 \) and \( x = -1 \).

Let's choose \( x = 0 \) and \( x = 1 \) as our points. 

1. **For \( x = 0 \):**

   Substitute \( x = 0 \) into the function:

   \[
   k(0) = (0)^2 + 5(0) + 4 = 0 + 0 + 4 = 4
   \]

   So, the point is \( (0, 4) \).

2. **For \( x = 1 \):**

   Substitute \( x = 1 \) into the function:

   \[
   k(1) = (1)^2 + 5(1) + 4 = 1 + 5 + 4 = 10
   \]

   So, the point is \( (1, 10) \).

**Summary:**

Two points on the graph of the parabola other than the vertex and \( x \)-intercepts are \( (0, 4) \) and \( (1, 10) \).

Would you like more details or have any questions?

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Here are some related questions you might consider:

1. How do you find the vertex of the parabola \( k(x) = x^2 + 5x + 4 \)?
2. What is the axis of symmetry for this parabola?
3. How can you determine the direction in which the parabola opens?
4. What is the y-intercept of the function \( k(x) = x^2 + 5x + 4 \)?
5. How do you graph the entire function \( k(x) = x^2 + 5x + 4 \)?
6. How do you find the minimum or maximum value of \( k(x) \)?
7. How do the points \( (0, 4) \) and \( (1, 10) \) relate to the shape of the parabola?
8. Can you express the function \( k(x) \) in factored form?

**Tip:** Choosing points near the vertex or intercepts helps in sketching a more accurate graph of the parabola.

Learn how to find two points on the graph of the quadratic function k(x) = x^2 + 5x + 4, excluding the vertex and x-intercepts. Explore detailed step-by-step solutions and understand the concept of parabolas in algebra. Suitable for high school students.

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