Question

How do you write a quadratic function in intercept form whose graph has x intercepts -7, -2 and passes through (-5, -6)?

Answer 1

`y=(x+7)(x+2)`

Explanation:

`"given the x-intercepts ( zeros) of a quadratic function"`

`"say "x=a" and "x=b`

`"then the factors are "(x-a)" and "(x-b)`

`"and the quadratic function can be expressed as a"`
`"product of the factors"`

`y=k(x-a)(x-b)`

`"where k is a multiplier and can be found if we are"`
`"given a point on the parabola"`

`"here "x=-7" and "x=-2`

`rArr(x+7),(x+2)" are the factors"`

`rArry=k(x+7)(x+2)`

`"to find k substitute "(-5,-6)" into the equation"`

`-6=k(2)(-3)=-6krArrk=1`

`rArry=(x+7)(x+2)larrcolor(red)" in intercept form"`