Question
Find the maximum value of the parabola: y = -3x^2 + 6x. Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Answers
GPT-4o mini
To find the maximum value of the parabola given by the equation \( y = -3x^2 + 6x \), we can use the vertex formula. The vertex \( x \)-coordinate of a parabola in the form \( y = ax^2 + bx + c \) is given by:
\[
x = -\frac{b}{2a}
\]
In our case, \( a = -3 \) and \( b = 6 \). Substituting in these values, we get:
\[
x = -\frac{6}{2 \cdot -3} = -\frac{6}{-6} = 1
\]
Next, we substitute \( x = 1 \) back into the equation to find the maximum value of \( y \):
\[
y = -3(1)^2 + 6(1)
\]
\[
y = -3 \cdot 1 + 6 \cdot 1
\]
\[
y = -3 + 6
\]
\[
y = 3
\]
Thus, the maximum value of the parabola is
\[
\boxed{3}.
\]
\[
x = -\frac{b}{2a}
\]
In our case, \( a = -3 \) and \( b = 6 \). Substituting in these values, we get:
\[
x = -\frac{6}{2 \cdot -3} = -\frac{6}{-6} = 1
\]
Next, we substitute \( x = 1 \) back into the equation to find the maximum value of \( y \):
\[
y = -3(1)^2 + 6(1)
\]
\[
y = -3 \cdot 1 + 6 \cdot 1
\]
\[
y = -3 + 6
\]
\[
y = 3
\]
Thus, the maximum value of the parabola is
\[
\boxed{3}.
\]