The vertex of the positive parabola turns at point (-2, -11)
Differentiate and equate to zero Hence y = x^2 + 4x - 12 dy/dx = 2x + 4 = 0 2x = -4 x = -2 Hence y = (-2)^2 +4(-2) - 12 y = 4 - 8 - 12 y = - 16 Hence the vertex is (x,y,) = ( -2,-16)
y=aX2+bX+c ---> y=X2-6X+5vertex formula is -b/2a( b=-6,a=1)vertex=-(-6)/2*1=6/2=3 y=32-6(3)+5---->y=-4so vertex is (3,4)
(3, -21)
y = 2x2 + 4x - 3 This equation describes a parabola. Because it's first term is positive, we know that it goes infinitely upward, and has a minimum that occurs at it's vertex. You can find it's vertex by taking it's derivative and solving for zero: y' = 4x + 4 0 = 4x + 4 0 = x + 1 x = -1 y = (-1)2 + 4(-1) - 3 y = 1 - 4 - 3 y = -6 So the vertex is at (-1, -6), which means that y ≥ -6
The vertex of the positive parabola turns at point (-2, -11)
Y = X2 - 4X - 5set to zeroX2 - 4X - 5 = 0X2 - 4X = 5halve the linear term ( - 4 ) then square it and add that result to both sidesX2 - 4X + 4 = 5 + 4factor on the left and gather terms together on the right(X - 2)2 = 9(X - 2)2 - 9 = 0==============vertex form(2, - 9)======vertex
Differentiate and equate to zero Hence y = x^2 + 4x - 12 dy/dx = 2x + 4 = 0 2x = -4 x = -2 Hence y = (-2)^2 +4(-2) - 12 y = 4 - 8 - 12 y = - 16 Hence the vertex is (x,y,) = ( -2,-16)
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To find the extreme value of the parabola y = x2 - 4x + 3 ...(1) Take the derivative of the equation.y = x2 - 4x + 3y' = 2x - 4(2) Set the derivative = 0 and solve for x.y' = 2x - 40 = 2x - 42x = 4x = 4/2x = 2(3) Plug this x value back into the original equation to find the associated y coordinate.x = 2y = x2 - 4x + 3y = (2)2 - 4(2) + 3y = 4 - 8 + 3y = -1So the vertex is at (2, -1).
y=aX2+bX+c ---> y=X2-6X+5vertex formula is -b/2a( b=-6,a=1)vertex=-(-6)/2*1=6/2=3 y=32-6(3)+5---->y=-4so vertex is (3,4)
(3, -21)
y = 4x-3
y = 2x2 + 4x - 3 This equation describes a parabola. Because it's first term is positive, we know that it goes infinitely upward, and has a minimum that occurs at it's vertex. You can find it's vertex by taking it's derivative and solving for zero: y' = 4x + 4 0 = 4x + 4 0 = x + 1 x = -1 y = (-1)2 + 4(-1) - 3 y = 1 - 4 - 3 y = -6 So the vertex is at (-1, -6), which means that y ≥ -6
Assuming the missing symbol there is an equals sign, then we have: y - 2x2 - 4x = 4 We can find it's vertex very easily by solving for y, and finding where it's derivative equals zero: y = 2x2 + 4x + 4 y' = 4x + 4 0 = 4x + 4 x = -1 So the vertex occurs Where x = -1. Now we can plug that back into the original equation to find y: y = 2x2 + 4x + 4 y = 2 - 4 + 4 y = 2 So the vertex is at the point (-1, 2)
y=4x-12-3 is the equation of a straight line. It does not have a vertex. Did you mean y=x squared - 12x - 3 ?
y = x2 - 4x + 4 = (x - 2)2 has one repeated root