Which of the following coordinate pairs is a point on the parabola y= -4x^ - 53x - 56?
O (-4, -56).
O (-4, 220)
O (-1, -7)
O (-1, 13)
To determine if a coordinate pair is a point on the given parabola, we can substitute the x and y values into the equation y = -4x^2 - 53x - 56 and check if the equation holds true.
Let's check each pair:
For O (-4, -56):
y = -4(-4)^2 - 53(-4) - 56 = -4(16) + 212 - 56 = -64 + 212 - 56 = 92, which is not equal to -56.
So, O (-4, -56) is not a point on the parabola.
For O (-4, 220):
y = -4(-4)^2 - 53(-4) - 56 = -4(16) + 212 - 56 = -64 + 212 - 56 = 92, which is not equal to 220.
So, O (-4, 220) is not a point on the parabola.
For O (-1, -7):
y = -4(-1)^2 - 53(-1) - 56 = -4(1) + 53 - 56 = -4 + 53 - 56 = -7, which is equal to -7.
So, O (-1, -7) is a point on the parabola.
For O (-1, 13):
y = -4(-1)^2 - 53(-1) - 56 = -4(1) + 53 - 56 = -4 + 53 - 56 = -7, which is not equal to 13.
So, O (-1, 13) 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 O (-1, -7).
To determine which coordinate pair is a point on the parabola y = -4x^2 - 53x - 56, we can substitute the x and y values of each pair into the equation and check if the equation holds true.
Let's evaluate each option:
Option O (-4, -56):
y = -4(-4)^2 - 53(-4) - 56
y = -4(16) + 212 - 56
y = -64 + 212 - 56
y = 88 - 56
y = 32
Since 32 is not equal to -56, this option is not a point on the parabola.
Option O (-4, 220):
y = -4(-4)^2 - 53(-4) - 56
y = -4(16) + 212 - 56
y = -64 + 212 - 56
y = 88 - 56
y = 32
Again, 32 is not equal to 220, so this option is not a point on the parabola.
Option O (-1, -7):
y = -4(-1)^2 - 53(-1) - 56
y = -4(1) + 53 - 56
y = -4 + 53 - 56
y = 49 - 56
y = -7
The y-value of -7 matches the given coordinate pair, so this option is a point on the parabola.
Option O (-1, 13):
y = -4(-1)^2 - 53(-1) - 56
y = -4(1) + 53 - 56
y = -4 + 53 - 56
y = 49 - 56
y = -7
The y-value of -7 does not match the given coordinate pair, so this option is not a point on the parabola.
Therefore, the coordinate pair that is a point on the parabola y = -4x^2 - 53x - 56 is O (-1, -7).
To determine if a given point is on the parabola, we need to substitute the x and y values of the point into the equation of the parabola and check if the equation holds true. Let's do this for each of the given options.
Option O (-4, -56):
Substituting x = -4 and y = -56 into the equation y = -4x^2 - 53x - 56, we get:
-56 = -4(-4)^2 - 53(-4) - 56
Simplifying the equation:
-56 = -4(16) + 212 - 56
-56 = -64 + 212 - 56
-56 = -120 + 212
-56 = 92
Since -56 is not equal to 92, this coordinate pair (-4, -56) is not a point on the parabola.
Option O (-4, 220):
Substituting x = -4 and y = 220 into the equation y = -4x^2 - 53x - 56, we get:
220 = -4(-4)^2 - 53(-4) - 56
Simplifying:
220 = -4(16) + 212 - 56
220 = -64 + 212 - 56
220 = -120 + 212
220 = 92
Since 220 is not equal to 92, this coordinate pair (-4, 220) is not a point on the parabola.
Option O (-1, -7):
Substituting x = -1 and y = -7 into the equation y = -4x^2 - 53x - 56, we get:
-7 = -4(-1)^2 - 53(-1) - 56
Simplifying:
-7 = -4(1) + 53 - 56
-7 = -4 + 53 - 56
-7 = 49 - 56
-7 = -7
Since -7 is equal to -7, this coordinate pair (-1, -7) is a point on the parabola.
Option O (-1, 13):
Substituting x = -1 and y = 13 into the equation y = -4x^2 - 53x - 56, we get:
13 = -4(-1)^2 - 53(-1) - 56
Simplifying:
13 = -4(1) + 53 - 56
13 = -4 + 53 - 56
13 = 49 - 56
13 = -7
Since 13 is not equal to -7, this coordinate pair (-1, 13) is not a point on the parabola.
Therefore, the only point that lies on the parabola y = -4x^2 - 53x - 56 is (-1, -7).