Question

How do you write a quadratic function in intercept form who has x intercepts 4, 6 and passes through points (5,-2)?

Answer 1

`y=2(x-4)(x-6)`

Explanation:

`"given x-intercepts "x=b" and "x=c`

`"we can express the factors as "(x-b)" and "(x-c)`

`"and the quadratic function as the product of the factors"`

`rArry=a(x-c)(x-b)larrcolor(blue)" a is a constant"`

`"here the intercepts are "x=4" and "x=6`

`rArry=a(x-4)(x-6)`

`"to find a substitute "(5,-2)" into the equation"`

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

`"the quadratic function is therefore"`

`y=2(x-4)(x-6)larrcolor(red)" in intercept form"`
graph{2(x-4)(x-6) [-10, 10, -5, 5]}