What is the axis of symmetry and vertex for the graph #y = 2(x – 4)^2 + 7#?

1 Answer
Daniel Tan
May 2, 2018

#:. x = 4#

#:. (4,7)#

Explanation:

The answers can be found through the equation itself.

#y = a(x-b)^2+c#

For axis of symmetry, you just need to look at the terms inside the bracket once you have factorized the equation to its basic state.

A.O.S
#=> (x-4)#

#:. x = 4#

For the point of vertex, which can be a minimum point or a maximum point which can be told by the value of #a#

#-a# = maximum point ; #a# = minimum point

The value of #c# in your equation actually represents the #y-#coordinate of your highest/lowest point.

Thus, your #y-#coordinate is #7#

Point of vertex? Combine the value of your axis of symmetry with your #c# value. This is because the axis of symmetry is always in the middle of the curve, therefore it is also the highest/lowest point of your curve.

#:. (4,7)#

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