You can find the x-coordinate of it's vertex by taking it's derivative and solving for zero: y = -3x2 + 12x - 5 y' = -6x + 12 0 = -6x + 12 6x = 12 x = 2 Now that we have it's x coordinate, we can plug it back into the original equation to find it's y coordinate: y = -3x2 + 12x - 5 y = -3(2)2 + 12(2) + 5 y = -12 + 24 + 5 y = 17 So the vertex of the parabola y = -3x2 + 12x - 5 occurs at the point (2, 17).
Differentiate the function with respect to x: d/dx (x3 - 2x2 - 5x + 6) = 3x2 - 4x - 5 Set this derivative = 0 and solve. 3x2 - 4x - 5 = 0 implies that x = -0.7863 or 2.1196 (to 4 dp)
6 - y + 5y - 6y = 0 6 = y -5y + 6y 6 = -4y + 6y 6 = 2y 6/2 = y 3 = y
Yes. (Assuming that -3x2 is the best representation of 3x2 that this browser will allow.)
y = -6 is a horizontal line that cuts the y-axis at -6.
(x2 - 2)(y - 3)
Let y = x3 - 8, then y' = 3x2 + 0 = 3x2.
y=3(2+x) y= 6+3x Switch x and y x = 6+3y solve for y x-6 = 3y 3y = x-6 y = (x-6)/3 f^-1(x) = (x-6)/3 is the inverse function.
-6to work it out: remember BIDMASso 3x2=6! then 6-12=-6
3 * x * x * y
6
The rule you have described is likely a linear function. When the input is -2 and the output is 4, it means that the function relates these two values through a specific mathematical operation. To determine the exact rule, we need more data points or information about the function's form (e.g., y = mx + b for a linear function).
6
(2x3)+(3x5)-(3x2)= 2x3=6 3x5=15 3x2=6 So..... 6x25-6= 6x25=150 150+6=156
3x2 - 2y2 = 9x2 + 4y2 - 12xy (subtract 3x2 and add 2y2 to both sides) 0 = 9x2 -3x2 + 4y2 + 2y2 - 12xy 0 = 6x2 + 6y2 - 12xy (divide by 6 to both sides) 0 = x2 + y2 - 12xy or x2 - 2xy + y2 = 0 (x - y)(x - y) = 0 x - y = 0 x = y
3x2=6+38=44
3x2 if it is in parentheses