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Evaluate the polynomial equation [tex]y=\frac{1}{2} x^3+2 x^2+4 x-6[/tex] for each value of [tex]x[/tex]. Click on the numbers you want to select and drag them into the boxes.

If [tex]x=2[/tex], then [tex]y=\frac{1}{2} x^3+2 x^2+4 x-6=\square[/tex]

If [tex]x=3[/tex], then [tex]y=\frac{1}{2} x^3+2 x^2+4 x-6=\square[/tex]

14

37.5

18

-10

21.3



Answer :

GinnyAnswer
Let's evaluate the polynomial equation [tex]\(y=\frac{1}{2}x^3+2x^2+4x-6\)[/tex] for the given values of [tex]\(x\)[/tex].

### When [tex]\(x = 2\)[/tex]:
1. Start by substituting [tex]\(x = 2\)[/tex] into the polynomial:
[tex]\[ y = \frac{1}{2}(2)^3 + 2(2)^2 + 4(2) - 6 \][/tex]

2. Evaluate each term:
- [tex]\(\frac{1}{2}(2)^3 = \frac{1}{2} \times 8 = 4\)[/tex]
- [tex]\(2(2)^2 = 2 \times 4 = 8\)[/tex]
- [tex]\(4(2) = 8\)[/tex]
- The constant term is [tex]\(-6\)[/tex]

3. Add the evaluated terms together:
[tex]\[ y = 4 + 8 + 8 - 6 = 14 \][/tex]

Therefore, when [tex]\(x = 2\)[/tex], [tex]\(y = 14\)[/tex].

### When [tex]\(x = 3\)[/tex]:
1. Substitute [tex]\(x = 3\)[/tex] into the polynomial:
[tex]\[ y = \frac{1}{2}(3)^3 + 2(3)^2 + 4(3) - 6 \][/tex]

2. Evaluate each term:
- [tex]\(\frac{1}{2}(3)^3 = \frac{1}{2} \times 27 = 13.5\)[/tex]
- [tex]\(2(3)^2 = 2 \times 9 = 18\)[/tex]
- [tex]\(4(3) = 12\)[/tex]
- The constant term is [tex]\(-6\)[/tex]

3. Add the evaluated terms together:
[tex]\[ y = 13.5 + 18 + 12 - 6 = 37.5 \][/tex]

Therefore, when [tex]\(x = 3\)[/tex], [tex]\(y = 37.5\)[/tex].

### Final Answers:
- If [tex]\(x = 2\)[/tex], then [tex]\(y = 14\)[/tex].
- If [tex]\(x = 3\)[/tex], then [tex]\(y = 37.5\)[/tex].

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