Zeros or X-Intercepts 

To find the x intercepts in a parabola given a factored equation we will need to isolate x by replacing the y co-ordinate as 0. In this equation the x intercepts

are given to you thus, leaving you just to solve the equation.

 

Ex:       y = (x - 10)(x + 4)

      0 = (x - 10)         0 = (x +4) 

        10 = x                  -4 = x 

 

Tip  

When plotting  y = (x-9)(x+8), you just need to plot the -9 on 9 and 8 on -8 on the graph. Just flip the signs and plot it on the graph. 

 

Axis of Symmetry 

The axis of symmetry is a vertical line that separates the paraballa in two equal halves. 

 

 

You need to take the zeros (x-intercepts) that are given to you and plug it into the equation x = s+r/2 and you will have the AOS. Lets take the equation form zeros from the above problem: x = 10+ (-4)/2

                                            = 3

Therefore the AOS is 3 

 

Optimal Value

 

Now that we have our AOS we can sub it in to our equation so that we can get our optimal value which is our y co-ordinate.

 

Lets use the above problem: y = (3 - 10)(3 + 4) 

                                                = (-7)(7)

                                = -44

Therefore the vertex is (3, -44)