determine the maximum or the minimum of
a)2x^2+12x
2x^2+10 maybe?
2x^2+12x
= 2(x^2 + 6x)
= 2(x^2 + 6x + 9 - 90)
= 2( (x+3)^2 - 9)
= 2(x+3)^2 - 18
Minimum value of -18 when x = -3
To determine the maximum or minimum of the quadratic function 2x^2 + 12x, we need to find the vertex of the parabolic curve.
Step 1: Calculate the x-coordinate of the vertex (-b/2a).
In the given equation, a = 2 and b = 12.
x = -12 / (2 * 2)
x = -12 / 4
x = -3
Step 2: Plug the x-coordinate back into the equation to find the y-coordinate.
y = 2(-3)^2 + 12(-3)
y = 2(9) - 36
y = 18 - 36
y = -18
The vertex of the parabolic curve is at (-3, -18). Since the coefficient of x^2 is positive (a = 2 > 0), this means the parabola opens upward, indicating that the vertex represents the minimum point.
Therefore, the minimum value of the function 2x^2 + 12x is -18, which occurs at x = -3.