Find the coordinates of the turning point for the equation of the graph below. y=x2+14x+33
+37084 Hello..... you can graph it on this calculator (or others)
to find turning point ~ (-7, -16)
or you can take the derivative (which results in the equation of the SLOPE of the fxn) and set it = 0 to get
2x + 14 = 0
2x=-14
x= -7 then substitute into the ORIGINAL equation to get 'y' at that point:
y= x^2 + 14x +33 = 49 - 98 +33 = -16
ANOTHER way is to find the 'zeroes' using the quadratic formula or factor the equation into
(x+11)(x+3) to find the ZEROES as -11 and -3 the turning point is exactly between these two at x=-7
then substitute - 7 into the equation to get y = -16
+129838 Since this is a parabola that the turns upwards, the turning point occurs at the vertex. The x coordinate of the vertex can be found as :
-b/ [ 2a] = -14 / [2 (1)] = -14 / 2 = -7
The y coordinate of the vertex can be found by putting the x coordinate value back into the function
(-7)^2 + 14 (-7) + 33 =
49 - 98 + 33 =
-49 + 33 =
-16
So.......the turning point is ( -7, -16)
