Question

Find the missing values in the factored form of q(x), given its graph.

q(x) =(x+4)(x+__)(x-__)

Answer 1

To find the missing values in the factored form of \( q(x) = (x+4)(x+__)(x-__) \) given its graph, you will need to look for the x-intercepts (where the graph crosses the x-axis) or any given information about the roots of the polynomial represented by \( q(x) \).

In the given factored form, the term \( (x+4) \) indicates a root at \( x = -4 \). The other two terms, \( (x+__) \) and \( (x-__) \), imply there are two more roots, one positive and one negative.

1. **Identify x-intercepts:** If you have access to the graph, identify the x-intercepts. Suppose the graph shows x-intercepts at \( x = -4 \), \( x = -2 \), and \( x = 3 \).

- From \( (x+4) \) the root is \( -4 \).
- From \( (x+(-2)) \), the root would be \( -2 \).
- From \( (x-3) \), the root is \( 3 \).

2. **Substituting into the factored form:** The two missing values in \( q(x) = (x+4)(x+__)(x-__) \) based on the x-intercepts would be:
- \( (x + 2) \) for the root \( -2 \)
- \( (x - 3) \) for the root \( 3 \)

So the complete factored form would be \( q(x) = (x+4)(x+2)(x-3) \).

3. **Final Answer:** The missing values are:
- For \( x + __ \): \( 2 \)
- For \( x - __ \): \( 3 \)

Thus, \( q(x) = (x+4)(x+2)(x-3) \). If you have specific values based on the graph or x-intercepts, please provide those for precise identification.