Question

Which of the following are coordinate pairs of y = -4x^2 - 53x - 56

-4, -56

-1, -7

-4, -220

-1, 13

Answer 1

To determine which of the given coordinate pairs \((x, y)\) are on the curve defined by the equation \(y = -4x^2 - 53x - 56\), we will substitute each \(x\) value into the equation and see if the corresponding \(y\) value matches.

1. For the pair \((-4, -56)\):
\[
y = -4(-4)^2 - 53(-4) - 56
\]
\[
= -4(16) + 212 - 56
\]
\[
= -64 + 212 - 56
\]
\[
= 92 \quad (\text{not } -56)
\]

2. For the pair \((-1, -7)\):
\[
y = -4(-1)^2 - 53(-1) - 56
\]
\[
= -4(1) + 53 - 56
\]
\[
= -4 + 53 - 56
\]
\[
= -7 \quad (\text{correct})
\]

3. For the pair \((-4, -220)\):
\[
y = -4(-4)^2 - 53(-4) - 56
\]
(Already calculated above, \(y = 92\) which is not \(-220\))
\[
\text{So, this is not correct.}
\]

4. For the pair \((-1, 13)\):
\[
y = -4(-1)^2 - 53(-1) - 56
\]
(Already calculated above, \(y = -7\) which is not \(13\))
\[
\text{So, this is not correct.}
\]

In conclusion, the valid coordinate pair that lies on the curve \(y = -4x^2 - 53x - 56\) is:
- \((-1, -7)\)