Which of the following coordinate pairs is a point on the parabola y=−4x^2−53x−56

Question

Which of the following coordinate pairs is a point on the parabola y=−4x^2−53x−56

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3 answers
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Answer 1

Bot GPT 3.5 answered
1 year ago

To determine if a coordinate pair is on the parabola, we need to substitute the x-coordinate into the equation for x and see if it matches the y-coordinate.

a) (-5, -36)
Substituting x = -5 into the equation:
y = -4(-5)^2 - 53(-5) - 56
y = -4(25) + 265 - 56
y = -100 + 265 - 56
y = 109

Since the resulting y-coordinate does not match -36, (-5, -36) is not on the parabola.

b) (-3, 2)
Substituting x = -3 into the equation:
y = -4(-3)^2 - 53(-3) - 56
y = -4(9) + 159 - 56
y = -36 + 159 - 56
y = 67

Since the resulting y-coordinate does not match 2, (-3, 2) is not on the parabola.

c) (0, -56)
Substituting x = 0 into the equation:
y = -4(0)^2 - 53(0) - 56
y = 0 - 0 - 56
y = -56

Since the resulting y-coordinate matches -56, (0, -56) is on the parabola. Answer: \boxed{(0, -56)}.

Answer 2

Step-by-Step Bot answered
1 year ago

To identify which coordinate pair is a point on the parabola y = -4x^2 - 53x - 56, we need to substitute each x-coordinate into the equation and check if the corresponding y-coordinate matches. Let's check each coordinate pair one by one:

Coordinate pair (0, -56):
Substituting x = 0 into the equation:
y = -4(0)^2 - 53(0) - 56
y = -0 - 0 - 56
y = -56

The y-coordinate matches, so (0, -56) is a point on the parabola.

Coordinate pair (1, -109):
Substituting x = 1 into the equation:
y = -4(1)^2 - 53(1) - 56
y = -4 - 53 - 56
y = -113

The y-coordinate does not match, so (1, -109) is not a point on the parabola.

Coordinate pair (-2, -56):
Substituting x = -2 into the equation:
y = -4(-2)^2 - 53(-2) - 56
y = -4 * 4 + 106 - 56
y = -16 + 106 - 56
y = 34

The y-coordinate does not match, so (-2, -56) is not a point on the parabola.

Therefore, the only coordinate pair that is a point on the parabola y = -4x^2 - 53x - 56 is (0, -56).

Answer 3

Explain Bot answered
1 year ago

To determine which of the given coordinate pairs is a point on the parabola y = -4x^2 - 53x - 56, we can substitute the x-coordinate and y-coordinate from each pair into the equation and check if the equation holds true.

Let's go through each coordinate pair one by one:

1) (-2, 6)
To check if (-2, 6) is on the parabola, we substitute x = -2 and y = 6 into the equation:
6 = -4(-2)^2 - 53(-2) - 56

Simplifying the equation:
6 = -4(4) + 106 - 56
6 = -16 + 50
6 = 34

Since 6 is not equal to 34, the point (-2, 6) does not lie on the parabola y = -4x^2 - 53x - 56.

2) (1, -101)
To check if (1, -101) is on the parabola, we substitute x = 1 and y = -101 into the equation:
-101 = -4(1)^2 - 53(1) - 56

Simplifying the equation:
-101 = -4 - 53 - 56
-101 = -113 - 56
-101 = -169

Since -101 is not equal to -169, the point (1, -101) does not lie on the parabola y = -4x^2 - 53x - 56.

3) (5, -151)
To check if (5, -151) is on the parabola, we substitute x = 5 and y = -151 into the equation:
-151 = -4(5)^2 - 53(5) - 56

Simplifying the equation:
-151 = -4(25) - 265 - 56
-151 = -100 - 265 - 56
-151 = -421 - 56
-151 = -477

Since -151 is equal to -477, the point (5, -151) lies on the parabola y = -4x^2 - 53x - 56.

Therefore, the coordinate pair (5, -151) is a point on the parabola y = -4x^2 - 53x - 56.