Which of the following coordinate pairs is a point on the parabola
y=7x^2+32x-19
1. (-1,-40)
2. (2,73)
3. (-3,52)
To determine if a coordinate pair is a point on the parabola, we substitute the x-coordinate into the equation and check if the resulting y-coordinate matches.
For coordinate pair (-1,-40):
Substituting x = -1 into the equation:
y = 7(-1)^2 + 32(-1) - 19
y = 7(1) - 32 - 19
y = 7 - 32 - 19
y = -45
The resulting y-coordinate of -45 does not match the given coordinate pair of (-1,-40). Therefore, (-1,-40) is not a point on the parabola.
For coordinate pair (2,73):
Substituting x = 2 into the equation:
y = 7(2)^2 + 32(2) - 19
y = 7(4) + 64 - 19
y = 28 + 64 - 19
y = 93 - 19
y = 74
The resulting y-coordinate of 74 matches the given coordinate pair of (2,73). Therefore, (2,73) is a point on the parabola.
For coordinate pair (-3,52):
Substituting x = -3 into the equation:
y = 7(-3)^2 + 32(-3) - 19
y = 7(9) - 96 - 19
y = 63 - 96 - 19
y = -32
The resulting y-coordinate of -32 matches the given coordinate pair of (-3,52). Therefore, (-3,52) is a point on the parabola.
In summary, the coordinate pairs that are points on the parabola y = 7x^2 + 32x - 19 are:
2. (2,73)
3. (-3,52)