Which of the following coordinate pairs is a point on the parabola y = -4x^2-53x -56?
• (-4,220)
• (-1,-7)
• (-4,-56)
• (-1,13)
To determine if a given coordinate pair is a point on a parabola, we substitute the values of x and y into the equation of the parabola and check if the equation is satisfied.
Let's check each coordinate pair:
1. (-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 + 156 - 56
220 = 92 - 56
220 = 36
The equation is not satisfied, so (-4,220) is not a point on the parabola.
2. (-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
The equation is satisfied, so (-1,-7) is a point on the parabola.
3. (-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 = 148 - 56
-56 = 92
The equation is not satisfied, so (-4,-56) is not a point on the parabola.
4. (-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
The equation is not satisfied, so (-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 (-1,-7).