How do you find the axis of symmetry, and the maximum or minimum value of the function # y=-x^2+2x+3#?

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Answer 1 · 2017-06-04T16:21:55

Line of symmetry is #x = 1# and the maximum value is at #(1,4)#

#y = ax^2 +bx +c# is the standard form of the equation of a parabola.

You can find the line of symmetry by using the formula:

#x = (-b)/(2a)#

So, for #y = -x^2 +2x +3" "x = (-2)/(2(-1))#

#x = 1#

This also gives you the #x#-co-ordinate of the vertex.
Substitute #x =1# to find #y#

#y = -(1)^2 +2(1) +3" "rarr y =4#

We see that #a < 0#, which means that the graph has a maximum turning point with the arms open downwards.

The point #(1,4)# is the maximum value for the function.