How do you find the axis of symmetry, and the maximum or minimum value of the function G(x) = x ^ 2 - 6?

1 Answer
May 8, 2016

Axis of symmetry is: x=0
Vertex is a minimum at (x,y)->(0,-6)

Explanation:

Consider the standard form: " "y=ax^2+bx+c

Given equation:" "y=x^2-6

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color(brown)("Solved by understanding the effects of the parts of the formula")
Suppose you just had y=ax^2

The axis of symmetry is the y-axis

If ax^2>0 then the graph is of general shape uu so it has a minimum

If ax^2<0 then the graph is of general shape nn so it has a maximum.

color(blue)("In the given equation "ax^2 > 0 " so the vertex is a minimum")
Note that a=+1
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Suppose you had a term bx -> y=ax^2+bx

Then the axis of symmetry is moved from the y-axis by (-1/2)b

color(blue)("The given equation does not have a "bx" term so the axis of ")
color(blue)("symmetry is still the y-axis.")
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The constant c lifts or lowers the graph so that y_("intercept")=c

color(blue)("So for this equation the vertex coincides with the y-axis at ")
color(blue)(y=-6)

color(blue)(=> "Minimum "->(x,y)->(0,-6))

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