Question

How do you write a quadratic equation with x-intercepts: -1,-1 ; point: (2,-9) ?

Answer 1

`y=-x^2-2x-1`

Explanation:

`"given the x-intercepts (roots ) are " x=-1,x=-1`

`"then the factors are " (x+1),(x+1)=(x+1)^2`

`rArry=a(x+1)^2`

`"to find a, substitute " (2,-9)" into the equation"`

`rArr-9=a(2+1)^2`

`rArr9a=-9rArra=-1`

`rArry=-(x+1)^2larrcolor(red)" in intercept form"`

`"expanding and simplifying gives"`

`y=-x^2-2x-1larrcolor(red)" in standard form"`
graph{-(x+1)^2 [-10, 10, -5, 5]}