how to identify the axis

Question

how would I identify the axis of symmetry and the vertex using

 

          y = x^2 - 4x -32

 

 

please show steps

Answer 1

Hi again L;

y = x² - 4x -32

This is in the format of...

y=ax²+bx+c

The axis of symmetry is...

x=-b/2a

x=[-(-4)]/[(2)(1)]

x=4/2

x=2

y = x² - 4x -32

y=[2²]-[(4)(2)]-32

y=4-8-32

y=4-40

y=-36

(2,-36)

Answer 2

Hi L,

 

I'd like to offer another solution for y'all's consideration:  completing the square!

 

y = x² - 4x - 32

 

y = x² - 4x (+ 4  - 4) - 32

 

y = x² - 4x + 4 - 36

 

y = (x-2)² - 36

 

This form of the equation shows that the vertex is (2, -36), because the x-coordinate of the vertex is the one you plug in that makes the square term 0, in this case x=2*.  And -36 is what's left, so that's the y-coordinate of the vertex.

 

*Btw, for similar reasons, x=2 is also the axis of symmetry.

 

PS:  I recommend graphing this on graph paper to get more comfort w/ the concepts!  VISUALIZE! :)

Answer 3

 Axis of Symmetry :   Y = -b/2a

                                Y = 2

    

   It is vertical line that passes through vertex, parallel to Y - axis