Question

How do you write `y-5 = -2(x+1)^2` in intercept form?

Answer 1

`y=(x+1+1/2sqrt10)(x+1-1/2sqrt10)`

Explanation:

`"arrange into standard form "y=ax^2+bx+c ;a!=0`

`y-5=-2x^2-4x-2`

`rArry=-2x^2-4x+3larrcolor(blue)"in standard form"`

`"with "a=-2,b=-4" and "c=3`

`"find the roots (x-intercepts) by equating to zero"`

`rArr-2x^2-4x+3=0`

`"use the "color(blue)"quadratic formula"`

`x=(4+-sqrt(16+24))/-4=(4+-sqrt40)/-4=(4+-2sqrt10)/-4`

`rArrx=-1+-1/2sqrt10`

`y=(x-(-1-1/2sqrt10))(x-(-1+1/2sqrt10))`

`rArry=(x+1+1/2sqrt10)(x+1-1/2sqrt10)`