To solve this problem, we need to evaluate the given function [tex]\( h(x) = x^2 + 5x - 3 \)[/tex] at three specific values of [tex]\( x \)[/tex]: -1, 0, and -4. Then we will create ordered pairs [tex]\((x, h(x))\)[/tex] for each of these values.
Let's begin by calculating each value step-by-step:
1. Finding [tex]\( h(-1) \)[/tex]:
- Substitute [tex]\( x = -1 \)[/tex] into the function [tex]\( h(x) \)[/tex]:
[tex]\[
h(-1) = (-1)^2 + 5(-1) - 3
\][/tex]
- Calculate the value:
[tex]\[
h(-1) = 1 - 5 - 3 = -7
\][/tex]
- So, the ordered pair is [tex]\((-1, -7)\)[/tex].
2. Finding [tex]\( h(0) \)[/tex]:
- Substitute [tex]\( x = 0 \)[/tex] into the function [tex]\( h(x) \)[/tex]:
[tex]\[
h(0) = 0^2 + 5(0) - 3
\][/tex]
- Calculate the value:
[tex]\[
h(0) = 0 + 0 - 3 = -3
\][/tex]
- So, the ordered pair is [tex]\((0, -3)\)[/tex].
3. Finding [tex]\( h(-4) \)[/tex]:
- Substitute [tex]\( x = -4 \)[/tex] into the function [tex]\( h(x) \)[/tex]:
[tex]\[
h(-4) = (-4)^2 + 5(-4) - 3
\][/tex]
- Calculate the value:
[tex]\[
h(-4) = 16 - 20 - 3 = -7
\][/tex]
- So, the ordered pair is [tex]\((-4, -7)\)[/tex].
Summarizing our results, we have:
- [tex]\( h(-1) = -7 \)[/tex]
- [tex]\( h(0) = -3 \)[/tex]
- [tex]\( h(-4) = -7 \)[/tex]
Thus, the corresponding ordered pairs are:
[tex]\[
(-1, -7), (0, -3), (-4, -7)
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{B. \, (-1, -7), (0, -3), (-4, -7)}
\][/tex]
