Which polynomial has a graph that passes through the given points?
(–3, 10), (–1, 0), (0, –5), (3, 52)
(1 point)
Responses
y = x3 – 4x2 + 2x – 5
y = x 3 – 4 x 2 + 2 x – 5
y = x3 + 4x2 – 2x – 5
y = x 3 + 4 x 2 – 2 x – 5
y = x3 + 4x2 + 2x – 5
y = x 3 + 4 x 2 + 2 x – 5
y = x4 + 4x3 – 2x2 – 5x
To find the polynomial that passes through the given points, we need to substitute the x and y coordinates of each point into the equation and see which one satisfies all the points.
Let's try option D: y = x4 + 4x3 – 2x2 – 5x
(–3, 10):
10 = (-3)^4 + 4(-3)^3 - 2(-3)^2 - 5(-3)
10 = 81 - 108 - 18 + 15
10 = -30
This equation does not satisfy the first point, so option D is not correct.
Let's try option A: y = x3 – 4x2 + 2x – 5
(–3, 10):
10 = (-3)^3 – 4(-3)^2 + 2(-3) – 5
10 = -27 - 36 - 6 - 5
10 = -74
This equation also does not satisfy the first point, so option A is not correct.
Let's try option B: y = x3 + 4x2 – 2x – 5
(–3, 10):
10 = (-3)^3 + 4(-3)^2 - 2(-3) - 5
10 = -27 + 36 + 6 - 5
10 = 10
This equation satisfies the first point. Let's check the other points to confirm if it satisfies all points.
(–1, 0):
0 = (-1)^3 + 4(-1)^2 - 2(-1) - 5
0 = -1 + 4 + 2 - 5
0 = 0
This equation satisfies the second point.
(0, –5):
-5 = (0)^3 + 4(0)^2 - 2(0) - 5
-5 = 0 + 0 - 0 - 5
-5 = -5
This equation satisfies the third point.
(3, 52):
52 = (3)^3 + 4(3)^2 - 2(3) - 5
52 = 27 + 36 - 6 - 5
52 = 52
This equation satisfies the fourth point.
Therefore, the correct answer is y = x3 + 4x2 – 2x – 5.