Question

How do you write a quadratic equation with x-intercepts: -1,2 ; point: (1,4)?

Answer 1

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

Explanation:

`"the x-intercepts (roots) are"`

`x=-1" and " x=2`

`rArr(x+1)" and " (x-2)" are factors"`

`"the quadratic is the product of it's factors"`

`rArry=a(x+1)(x-2)larr" a is a constant"`

`"to find a substitute " (1,4)" into the equation"`

`rArr4=a(2)(-1)`

`rArr-2a=4rArra=-2`

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

`"distributing gives"`

`y=-2(x^2-x-2)`

`rArry=-2x^2+2x+4larrcolor(red)" in standard form"`
graph{-2x^2+2x+4 [-10, 10, -5, 5]}