Final answer:
To find the maximum value of the quadratic equation y = -2x² + 3x + 36, calculate the vertex (h, k) using the formula -b/(2a) which gives x = 0.75 and then plug it into the equation to find y = 37.125, the maximum value.
Step-by-step explanation:
The question is asking to find the minimum or maximum value of the quadratic equation y = -2x² + 3x + 36.
To find the minimum or maximum value of a quadratic equation, one can use the vertex form of a parabola.
The vertex of the parabola, given by the equation (h, k), provides the minimum or maximum value depending on the coefficient of x².
Since our equation has a negative coefficient of -2 for x², the parabola opens downwards, which means the vertex will give us the maximum value of y.
To find the vertex, we need the x-coordinate of the vertex which can be calculated by -b/(2a). For the equation y = -2x² + 3x + 36, a = -2 and b = 3.
So the x-coordinate of the vertex is -3/(2(-2)) = 0.75.
Substituting x = 0.75 back into the equation, we can find the y-coordinate which is the maximum value of y.
y = -2(0.75)² + 3(0.75) + 36 = -2(0.5625) + 2.25 + 36 = -1.125 + 2.25 + 36 = 37.125.
Therefore, the maximum value of the equation y = -2x² + 3x + 36 is 37.125.