Answer:
a) i) when x = -2, y = -4
ii) when x = -1, y = 0.75
iii) when x = 1, y = 1.25
iv) when x = 4, y = 2
b) graph A
Step-by-step explanation:
[tex]y = \frac{1}{4} {x}^{3} - {x}^{2} + 2[/tex]
1) when x = -2,
* substitute -2 into x
[tex]y = \frac{1}{4} {( - 2)}^{3} - {( - 2)}^{2} + 2[/tex]
[tex]y = - 2 - 4+ 2[/tex]
[tex]y = - 4[/tex]
2) when x = -1
* substitute -1 into x
[tex]y = \frac{1}{4} {( - 1)}^{3} - {( - 1)}^{2} + 2[/tex]
[tex]y = - \frac{1}{4} - 1 + 2[/tex]
[tex]y = \frac{3}{4} \: or \: 0.75[/tex]
3) when x = 1
* substitute 1 into x
[tex]y = \frac{1}{4} {( 1)}^{3} - {( 1)}^{2} + 2[/tex]
[tex]y = \frac{1}{4} - 1 + 2[/tex]
[tex]y = \frac{5}{4} \: or \: 1.25[/tex]
4) when x = 4
* substitute 4 into x
[tex]y = \frac{1}{4} {( 4)}^{3} - {( 4)}^{2} + 2[/tex]
[tex]y = 16 - 16 + 2[/tex]
[tex]y = 2[/tex]
