the equation describes the pattern shown in the table is y = x² + 2x - 3 (option D)
Step-by-step explanation:
To determine which of the equation describes the pattern shown in the table, we need to insert the values of x and confirm if we will get corresponding value of y in any of the equation.
Let's check the equations in the options: when x = -4, -2
a) y = x² – 11
when x = -4
y = (-4)² - 11
y = 16 - 11 = 5
when x = -2
y = (-2)² - 11
y = 4 - 11 = -7
equation is wrong
b) x² +3x -1
when x = -4
y = (-4)² -3(-4) - 1
y = 16 + 12 -1 = 27
when x = -2
y = (-2)² -3(-2) - 1
y = 4 + 6 -1 = 9
equation is wrong
c) y = x² – 1
when x = -4
y = (-4)² - 1
y = 16 - 1 = 15
equation is wrong
d) y = x² + 2x - 3
when x = -4
y = (-4)² +2(-4) - 3
y = 16 - 8 -3 = 5
when x = -2
y = (-2)² +2(-2) - 3
y = 4 - 4 - 3
y = -3
equation is right
e) y=x²-x-1
when x = -4
y = (-4)² -(-4) - 1
y = 16 +4 -1
y = 19
equation is wrong
Therefore, the equation describes the pattern shown in the table is y = x² + 2x - 3 (option D)