Question

Write y= -1(x-4.5)^2 + 15.25 in standered form

Answer 1

Given:

The equation is

`y=-1(x-4.5)^2+15.25`

To find:

The standard form of the given equation.

Solution:

We have,

`y=-1(x-4.5)^2+15.25`

It is a quadratic equation.

The standard form of a quadratic equation is
`y=ax^2+bx+c`. So, we need to write the given equation in this form.

`y=-(x-4.5)^2+15.25`

`y=-[x^2-2(x)(4.5)+(-4.5)^2]+15.25`
`[\because (a-b)^2=a^2-2ab+b^2]`

`y=-[x^2-9x+20.25]+15.25`

`y=-x^2+9x-20.25+15.25`

`y=-x^2+9x-5`

Therefore, the required equation in standard form is
`y=-x^2+9x-5`.