How do you write a quadratic equation with x-intercepts: 0,2 ; point: (3,-6) ?

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Answer 1 · 2017-05-01T08:34:04

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

The quadratic must have factors #x# and #(x-2)# in order to have the required #x#-intercepts.

So it can be written in the form:

#y = kx(x-2)#

for some constant #k# to be determined.

Substitute the given point #(3, -6)# to find:

#color(blue)(-6) = k(color(blue)(3))(color(blue)(3)-2) = 3k#

Divide both ends by #3# to find:

#k = -2#

So:

#y = -2x(x-2) = -2x^2+4x#

graph{(4x^2+y^2-0.01)(4(x-2)^2+y^2-0.01)(4(x-3)^2+(y+6)^2-0.01)(y+2x^2-4x) = 0 [-3.6, 6.4, -7.08, 2.92]}