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. should I enter x = (answer) or just (answer)

Answer 1

To find the maximum value of the parabola given by the equation \( y = -3x^2 + 6x \), we can use the vertex formula for a quadratic equation of the form \( y = ax^2 + bx + c \), where the x-coordinate of the vertex is given by \( x = -\frac{b}{2a} \).

Here, \( a = -3 \) and \( b = 6 \).

Calculating the x-coordinate of the vertex:

\[
x = -\frac{b}{2a} = -\frac{6}{2 \times -3} = -\frac{6}{-6} = 1
\]

Now, we need to find the maximum value of \( y \) by substituting \( x = 1 \) back into the equation:

\[
y = -3(1)^2 + 6(1)
\]
\[
y = -3(1) + 6
\]
\[
y = -3 + 6
\]
\[
y = 3
\]

Thus, the maximum value of the parabola is \( 3 \).

Since the question asks how to enter the answer, you just need to enter the maximum value as:

**3**