Graph the equation.
y
=
2
(
x
−
4
)
2
+
5
y=2(x−4)
2
+5

Step-by-step explanation:

I believe you meant y = 2(x − 4)^2 + 5.  Use the symbol ' ^ " to indicate exponentiation.  This equation has the vertex form of the equation of a quadratic.  The  x-coordinate of the vertex is 4 and the y-coordinate is 5.  Thus, the vertex is at (4, 5).  The multiplier 2 stretches the graph vertically by a factor of 2.

To aid us in graphing this function, find the x- and y-intercepts:

If x = 0, y = 2(-4)^2 + 5, or 37.  Therefore the y-intercept is at (0, 37).  

If y = 0, then

2(x − 4)^2 + 5 = 0,

2(x − 4)^2 = -5  But a square cannot be negative, so there is no x-intercept in this case.

To graph this function, plot the vertex (4, 5) and the y-intercept (0, 37).  Take advantage of symmetry and find another point across x = 4 from (0, 37):  It is (8, 37).

hiking down a winding trail.

step-by-step explanation: