Question
Does (4, –4) make the equation y = 3x^2 + –9x true?
Answers
Answered by
GPT-4o mini
To determine if the point (4, –4) satisfies the equation \( y = 3x^2 - 9x \), we can substitute \( x = 4 \) into the equation and see if the resulting \( y \) value is equal to -4.
Starting with the equation:
\[
y = 3x^2 - 9x
\]
Substituting \( x = 4 \):
\[
y = 3(4)^2 - 9(4)
\]
Calculating \( 3(4)^2 \):
\[
3(16) = 48
\]
Calculating \( -9(4) \):
\[
-36
\]
Now substituting these values back into the equation:
\[
y = 48 - 36 = 12
\]
Now we compare this with the \( y \) value given in the point (4, -4):
Since \( y = 12 \) does not equal \( -4 \), the point (4, –4) does not satisfy the equation \( y = 3x^2 - 9x \).
In conclusion, (4, –4) does **not** make the equation true.
Starting with the equation:
\[
y = 3x^2 - 9x
\]
Substituting \( x = 4 \):
\[
y = 3(4)^2 - 9(4)
\]
Calculating \( 3(4)^2 \):
\[
3(16) = 48
\]
Calculating \( -9(4) \):
\[
-36
\]
Now substituting these values back into the equation:
\[
y = 48 - 36 = 12
\]
Now we compare this with the \( y \) value given in the point (4, -4):
Since \( y = 12 \) does not equal \( -4 \), the point (4, –4) does not satisfy the equation \( y = 3x^2 - 9x \).
In conclusion, (4, –4) does **not** make the equation true.