Which of the following coordinate pairs is a point on the parabola y=−4x2−53x−56 ?(1 point) Responses (−1,−7) left parenthesis negative1 comma negative 7 right parenthesis (−1,13) left parenthesis neagtive 1 comma 13 right parenthesis (−4,−56) left parenthesis negative 4 comma negative 56 right parenthesis (−4,220) left parenthesis negative 4 comma 220 right parenthesis
To find whether a point is on the parabola y=−4x^2−53x−56, substitute the x and y values of the point into the equation and see if it is satisfied.
For option 1: (-1, -7)
y = -4(-1)^2 - 53(-1) - 56
y = -4 + 53 - 56
y = -4 ≠ -7
For option 2: (-1, 13)
y = -4(-1)^2 - 53(-1) - 56
y = -4 + 53 - 56
y = -4 ≠ 13
For option 3: (-4, -56)
y = -4(-4)^2 - 53(-4) - 56
y = -64 + 212 - 56
y = -64 ≠ -56
For option 4: (-4, 220)
y = -4(-4)^2 - 53(-4) - 56
y = -64 + 212 - 56
y = 92 ≠ 220
None of the given options are points on the parabola 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-value into the equation and check if it matches the corresponding y-value.
Let's evaluate each option:
1. (-1, -7): Plug in x = -1 into the equation:
y = -4(-1)^2 - 53(-1) - 56
y = -4 + 53 - 56
y = -4
The y-value (-7) does not match the calculated value (-4). Therefore, (-1, -7) is not a point on the parabola.
2. (-1, 13): Substitute x = -1 into the equation:
y = -4(-1)^2 - 53(-1) - 56
y = -4 + 53 - 56
y = -7
The calculated value (-7) matches the given y-value (13). Thus, (-1, 13) is a point on the parabola.
3. (-4, -56): Substitute x = -4 into the equation:
y = -4(-4)^2 - 53(-4) - 56
y = -4(16) + 212 - 56
y = -64 + 212 - 56
y = 92
The calculated value (92) does not match the given y-value (-56). Therefore, (-4, -56) is not a point on the parabola.
4. (-4, 220): Plug in x = -4 into the equation:
y = -4(-4)^2 - 53(-4) - 56
y = -4(16) + 212 - 56
y = -64 + 212 - 56
y = 92
The calculated value (92) matches the given y-value (220). Therefore, (-4, 220) is a point on the parabola.
In summary, the coordinate pairs that are points on the parabola y = -4x^2 - 53x - 56 are (-1, 13) and (-4, 220).
To find out which of the given coordinate pairs is a point on the parabola y = -4x^2 - 53x - 56, you need to substitute the x and y values of each coordinate pair into the equation and check if the equation holds true.
Let's start with the first coordinate pair, (-1, -7):
First, substitute x = -1 and y = -7 into the equation:
-7 = -4(-1)^2 - 53(-1) - 56
Simplifying the equation:
-7 = -4 + 53 - 56
-7 = 49 - 56
-7 = -7
The equation holds true for the first coordinate pair. So, (-1, -7) is a point on the parabola y = -4x^2 - 53x - 56.
Now let's check the other coordinate pairs similarly:
(-1, 13):
Substitute x = -1 and y = 13 into the equation:
13 = -4(-1)^2 - 53(-1) - 56
13 = -4 + 53 - 56
13 = 49 - 56
13 = -7
The equation does not hold true for the second coordinate pair. So, (-1, 13) is not a point on the parabola y = -4x^2 - 53x - 56.
(-4, -56):
Substitute 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 = 148 - 56
-56 = 92
The equation does not hold true for the third coordinate pair. So, (-4, -56) is not a point on the parabola y = -4x^2 - 53x - 56.
(-4, 220):
Substitute 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 = 148 - 56
220 = 92
The equation does not hold true for the fourth coordinate pair. So, (-4, 220) is not a point on the parabola y = -4x^2 - 53x - 56.
Therefore, the only coordinate pair that is a point on the parabola y = -4x^2 - 53x - 56 is (-1, -7).