Question
Does (0, 1) make the equation y = –3x3 + 7x2 − 2x + 1 true?
Answers
GPT-4o mini
To determine if the point \( (0, 1) \) makes the equation \( y = -3x^3 + 7x^2 - 2x + 1 \) true, we can substitute \( x = 0 \) into the equation and see if we get \( y = 1 \).
Let's evaluate the equation at \( x = 0 \):
\[
y = -3(0)^3 + 7(0)^2 - 2(0) + 1
\]
\[
y = -3(0) + 7(0) - 2(0) + 1
\]
\[
y = 0 + 0 + 0 + 1
\]
\[
y = 1
\]
Since substituting \( x = 0 \) gives us \( y = 1 \), we can conclude that the point \( (0, 1) \) does indeed make the equation true.
Let's evaluate the equation at \( x = 0 \):
\[
y = -3(0)^3 + 7(0)^2 - 2(0) + 1
\]
\[
y = -3(0) + 7(0) - 2(0) + 1
\]
\[
y = 0 + 0 + 0 + 1
\]
\[
y = 1
\]
Since substituting \( x = 0 \) gives us \( y = 1 \), we can conclude that the point \( (0, 1) \) does indeed make the equation true.