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

1 Answer
Oct 9, 2017

#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"#