which of the following coordinate pairs is a point on the parabola y=-4x^2-53x-56?
a.(-4,-56)
b.(-1,13)
c.(-1,-7)
d.(-4,220)
To determine whether a coordinate pair is a point on the given parabola, substitute the x-value into the equation and see if the resulting y-value matches the given y-value.
a. (-4, -56)
Substituting x = -4 into the equation:
y = -4(-4)^2 - 53(-4) - 56
= -4(16) + 212 - 56
= -64 + 212 - 56
= -64 + 156
= 92
The y-value does not match -56.
b. (-1, 13)
Substituting x = -1 into the equation:
y = -4(-1)^2 - 53(-1) - 56
= -4(1) + 53 - 56
= -4 + 53 - 56
= -4 - 3
= -7
The y-value matches 13.
c. (-1, -7)
Substituting x = -1 into the equation:
y = -4(-1)^2 - 53(-1) - 56
= -4(1) + 53 - 56
= -4 + 53 - 56
= -4 - 3
= -7
The y-value matches -7.
d. (-4, 220)
Substituting x = -4 into the equation:
y = -4(-4)^2 - 53(-4) - 56
= -4(16) + 212 - 56
= -64 + 212 - 56
= -64 + 156
= 92
The y-value does not match 220.
Therefore, the correct answer is:
b. (-1, 13)
c. (-1, -7)
To find out which of the given coordinate pairs 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 see if it satisfies the equation.
Let's check each option:
a. (-4, -56)
Plugging in -4 for x and -56 for y:
-56 = -4(-4)^2 - 53(-4) - 56
-56 = -4(16) + 212 - 56
-56 = -64 + 212 - 56
-56 = -64 + 212 - 56
-56 = 92 - 56
-56 ≠ 36
b. (-1, 13)
Plugging in -1 for x and 13 for y:
13 = -4(-1)^2 - 53(-1) - 56
13 = -4(1) + 53 - 56
13 = -4 + 53 - 56
13 = 49 - 56
13 ≠ -7
c. (-1, -7)
Plugging in -1 for x and -7 for y:
-7 = -4(-1)^2 - 53(-1) - 56
-7 = -4(1) + 53 - 56
-7 = -4 + 53 - 56
-7 = 49 - 56
-7 ≠ -7
d. (-4, 220)
Plugging in -4 for x and 220 for y:
220 = -4(-4)^2 - 53(-4) - 56
220 = -4(16) + 212 - 56
220 = -64 + 212 - 56
220 = -64 + 212 - 56
220 ≠ 92
None of the given coordinate pairs satisfies the equation y = -4x^2 - 53x - 56.
To determine which of the given coordinate pairs is a point on the parabola y = -4x^2 - 53x - 56, we need to substitute the x and y values from each pair into the equation and see if the equation holds true.
Let's go through each option:
a. (-4, -56):
Substituting x = -4 and y = -56 into the equation:
-56 = -4(-4)^2 - 53(-4) - 56
-56 = -4(16) + 212 - 56
-56 = -64 + 212 - 56
-56 = -120 + 212
-56 = 92
Since -56 does not equal 92, this option is not a point on the parabola.
b. (-1, 13):
Substituting x = -1 and y = 13 into the equation:
13 = -4(-1)^2 - 53(-1) - 56
13 = -4(1) + 53 - 56
13 = -4 + 53 - 56
13 = 49 - 56
13 = -7
Since 13 does not equal -7, this option is not a point on the parabola.
c. (-1, -7):
Substituting x = -1 and y = -7 into the equation:
-7 = -4(-1)^2 - 53(-1) - 56
-7 = -4(1) + 53 - 56
-7 = -4 + 53 - 56
-7 = 49 - 56
-7 = -7
Since -7 equals -7, this option is a point on the parabola.
d. (-4, 220):
Substituting x = -4 and y = 220 into the equation:
220 = -4(-4)^2 - 53(-4) - 56
220 = -4(16) + 212 - 56
220 = -64 + 212 - 56
220 = -120 + 212
220 = 92
Since 220 does not equal 92, this option is not a point on the parabola.
Therefore, the answer is c. (-1, -7) is the only coordinate pair that is a point on the parabola y = -4x^2 - 53x - 56.