### Question Description

I need support with this Applied Mathematics question so I can learn better.

1.

Hi Class,

For my two chosen solutions to a quadratic equation, I am going to work with x = – 6 and x = – 10

Working backwards:

Step 1 : After choosing two solutions, set up your solutions just like this.

*y*

= ( x + 6 ) ( x + 10 )

Step 2: I multiply the solutions out using the FOIL method.

y = x^{2} + 10x + 6x + 60

y = x^{2} + 16x + 60

Step 3: Put into vertex form by completing the square.

y = a( x – h )^{2} + k (This is the vortex Form)

We need to find what is Half of 16

Half of 16 = 8

So, 16 + 8 = 24

We have:

y = x^{2} + 16x + 24 + 60 – 24 ( we bring 24 to both sides)

y = x^{2} + 16x + 36

y = (x + 8) (x + 8) + 36

y = (x + 8)^{2 }+ 36

h = – 8, k = 36

I hope this makes sense onhow I worked out the problem backwards. If I missed a step please let meknow so I can understand what happened and if it makes sense then thatis great.

2.

Hello Class,

My two chosen solutions are *x*=8

undefined*x*=?5

So working backwards:

*y*=(*x*?8)(*x*+5)

using the FOIL method:

*y*=*x*2?8*x*+5*x*?40

*y*=*x*2?3*x*?40

*y*=*x*2?3*x*+94?40?94

*y*=(*x*?32)(*x*?32)?1604?94

*y*=(*x*?32)2?1694

The simplified form would be:

*y*=(*x*?112)2?4214

using the vertex form above the vertex is:

This is a fun lesson and got to relearn information I had long forgotten.