Question 389917: Find the x-intercept of the parabola with vertex (-3,-18)and y-intercept(0,0).
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Standard form of the parabola,
y=A(x-h)^2 +k, (h,k) representing the (x,y) coordinates of the vertex
with given (h,k) = (-3,-18)
y=A(x+3)^2 -18
solving for A, using a given (x,y) point,(0,0) of the parabola,
0=A(0+3)^2-18
9A=18
A=2
equation of the parabola: y=2(x+3)^2-18
in another form, y=2(x^2+6x+9)-18
=2x^2+12x+18-18
=2x^2+12x=2x(x+6)
to find x-intercepts,set y=0
2x(x+6) =0
2x=0
x=0
x+6=0
x=-6
ans: parabola intercepts x-axis at 0 and -6
see graph below
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