Question
Does (–3, 0) make the equation y = x^2 + 7x + –3 true?
Answers
Answered by
GPT-4o mini
To determine if the point (-3, 0) satisfies the equation \( y = x^2 + 7x - 3 \), we need to substitute \( x = -3 \) into the equation and check if the result equals \( y = 0 \).
Starting with the equation:
\[
y = x^2 + 7x - 3
\]
Substituting \( x = -3 \):
\[
y = (-3)^2 + 7(-3) - 3
\]
Calculating each term:
\[
(-3)^2 = 9
\]
\[
7(-3) = -21
\]
Now substituting those values into the equation:
\[
y = 9 - 21 - 3
\]
Calculating the right side:
\[
y = 9 - 21 - 3 = 9 - 24 = -15
\]
Since we found \( y = -15 \) when \( x = -3 \), but we needed \( y = 0 \) for the point (-3, 0), the point does not satisfy the equation.
Therefore, the conclusion is:
No, the point (-3, 0) does not make the equation \( y = x^2 + 7x - 3 \) true.
Starting with the equation:
\[
y = x^2 + 7x - 3
\]
Substituting \( x = -3 \):
\[
y = (-3)^2 + 7(-3) - 3
\]
Calculating each term:
\[
(-3)^2 = 9
\]
\[
7(-3) = -21
\]
Now substituting those values into the equation:
\[
y = 9 - 21 - 3
\]
Calculating the right side:
\[
y = 9 - 21 - 3 = 9 - 24 = -15
\]
Since we found \( y = -15 \) when \( x = -3 \), but we needed \( y = 0 \) for the point (-3, 0), the point does not satisfy the equation.
Therefore, the conclusion is:
No, the point (-3, 0) does not make the equation \( y = x^2 + 7x - 3 \) true.