Zeroes 

To solve an equation given to us in standard form, one must put it in the quadratic equation which is:  -b+-√b²-4(a)(c)

             2(a)

This will allows us to find the x- intercepts in a standard form equation. 

 

For instance we may come along the equation: y= 2x​​​²+6x+3 

We would then need to plug it into

  = -6+-√6²-4(2)(3)

            2(2)

 = -6+-√16

         4

= -3-+4

      4

x = 0.25 or -1.75

 

Axis of Symmetry

To find the AOS we would need to extract information from the standard form equation and put it into the equation: -b/2a

x= 2x​​​²+6x+3 

x= -6/2(2)

x= -1.5 

 

 

Optimal Value

Now we just have to sub in the x - intercept from the last step to get our optimal value. 

 

y= 2(-1.5)​​​²+6(-1.5)+3 

y= 4.5 -9 +3

y= -2.5 

 

Vertex: (-1.5, -2.5)

 

Now we have completed how to find the vertex and x-intercepts when we encounter a standard form equation. 

 

Completing the Square to Turn to Vertex Form 

To change to vertex form we need a square. 

 

y= x² +6x +7 

 

we must devide b by two and then square it, add it into the equation just like I did:

 

y= (x² +6x + 9) -9 +7

 

y= (x+3)² -2  

 

Now it is in vertex form