Question

What polynomial has a graph that passes through the given points?

(-2, 2) (-1, -1) (1, 5) (3, 67)
A. y = -x^3 + 4x^2 + 2x - 2

B. y = x^3 + 4x^2 + 2x - 2

C. y = x^4 + 4x^3 + 2x^2 - 2x

Answer 1

The answer is B. y = x^3 + 4x^2 + 2x - 2

A line that passes through all given point is the correct choice. Now, substitute x and y in all of the choices:

B. y = x³ + 4x² + 2x - 2
Point 1: (-2, 2)
x = -2
y = 2
____
2 = (-2)³ + 4 *(-2)² + 2 * (-2) - 2
2 = -8 + 4 * 4 + (-4) - 2
2 = -8 + 16 - 4 - 2
2 = 2
_____

Point 2: (-1, -1)
x = -1
y = -1
____
-1 = (-1)³ + 4 *(-1)² + 2 * (-1) - 2
-1 = -1 + 4 * 1 + (-2) - 2
-1 = -1 + 4 - 2 - 2
-1 = -1
____

Point 3: (1, 5)
x = 1
y = 5
____
5 = (1)³ + 4 *(1)² + 2 * 1 - 2
5 = 1 + 4 * 1 + 2 - 2
5 = 1 + 4 + 2 - 2
5 = 5
____

Point 4: (3, 67)
x = 3
y = 67
____
67 = (3)³ + 4 *(3)² + 2 * (3) - 2
67 = 27 + 4 * 9 + 6 - 2
67 = 27 + 36 + 6 - 2
67 = 67

So, line B passes through all choices.