Find the maximum value of: y=-3x^2 -15x +1
in any parabola ax^2+bx+c=0, the max value is attained at x = -/2a.
So, here that would be when x = 15/-6 = -5/2
y(5/2) = 19.75
another way of solcinf the problem is by deriving and setting dy/dx=0...but the above sol. is easier that but its disadv. is you may forget the formula.. :D
To find the maximum value of the function y = -3x^2 - 15x + 1, we need to determine the vertex of the parabola.
A quadratic function in the form y = ax^2 + bx + c, where a, b, and c are constants, has a vertex at the point (-b/2a, f(-b/2a)), where f(x) is the given quadratic function.
In our case, a = -3, b = -15, and c = 1.
The x-coordinate of the vertex can be found using the formula x = -b/2a:
x = -(-15) / (2 * -3)
x = 15 / -6
x = -2.5
Now, substitute this x-value back into the equation to find the y-coordinate:
y = -3(-2.5)^2 - 15(-2.5) + 1
y = -3(6.25) + 37.5 + 1
y = -18.75 + 37.5 + 1
y = 19.75
Therefore, the maximum value of the function y = -3x^2 - 15x + 1 is 19.75, which occurs at the vertex (-2.5, 19.75).