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quadratic function f(x)=(x 2)^2-4 what is the axis

Algebra
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quadratic function f(x)=(x+2)^2-4 what is the axis

Nov 11th, 2014

I am assuming that you actually mean "axis of symmetry"

Note.  For a quadratic function in the Vertex Form:        f(x) = a(x - h)^2 + k

                                                                                       The equation for the axis of symmetry is    x = h


The quadratic function f(x) = (x + 2)^2 - 4 is in vertex form.  Meaning we can compare with f(x) = a(x - h)^2 + k to get our value of 'h'.  Then we can use this value to obtain your equation for the function's axis of symmetry.

                                        f(x) = (x + 2)^2 - 4             <Given quadratic function.  It is in vertex form>

                                        f(x) = a(x - h)^2 + k            <Compare give quadratic function with the vertex form>

                                        x + 2 = x -  h                      <We would compare the expressions in parenthesis>

                                       x + 2 - x = x - h - x              <Subtract both sides by x>

                                        2 = -h

                                       -2 = h                                  <Negate both sides>

                                        h = -2

Now that we have our value of h, we can obtain our equation for the axis of symmetry

                                       x = h                              <Equation for the axis of symmetry>

                                       x = -2                              <Substitute the value of h>


SOLUTION:      Equation for the axis of symmetry is  x = -2

Nov 11th, 2014

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