Question

What would be the standard for of the quadratic equation ?

Answer 1

The standard form of the quadratic equation is:
`y=ax^2+bx+c`.
To find the standard form from our table, we are going to find the constant term,
`c`, first. To do that we are going to look for the value of
`y` in or table in which
`x=0`. From our table we can infer that when
`x=0`
`y=-6`, so
`c=-6`.
So now we have:
`y=ax^2+bx-6`

Next, to find
`a` and
`b` we are going to use the points (1,2) and (3,0) from our table to create a system of equations:
- Using the point (1,2)

`[tex]y=ax^2+bx-6`[/tex]

`2=a(1)^2+b(1)-6`

`2=a+b-6`

`a+b=8` equation (1)
- Using the point (3,0):

`[tex]y=ax^2+bx-6`[/tex]

`0=a(3)^2+b(3)-6`

`0=9a+3b-6`

`9a+3b=6` equation (2)

Now we can solve our system of equations:
From equation (1)

`a+b=8`

`a=8-b` equation (3)

Replacing equation (3) in equation (2)

`9a+3b=6`

`9(8-b)+3b=6`

`72-9b+3b=6`

`72-6b=6`

`-6b=-66`

`b= (-66)/(-6)`

`b=11` equation (4)

Replacing equation (4) in equation (3)

`a=8-b`

`a=8-11`

`a=-3`

Putting all together:

`[tex]y=ax^2+bx-6`[/tex]

`y=-3x^2+11x-6`

We can conclude that the standard form of the quadratic equation from our table is:
`y=-3x^2+11x-6`