SOLUTION: Given the function y = ( x+3 ) ( x^2+3 x−3 ) find the coordinates of the points of intersection with the x-axis and y-axis. Please enter your answer as a set of coordi

Algebra ->  Graphs -> SOLUTION: Given the function y = ( x+3 ) ( x^2+3 x−3 ) find the coordinates of the points of intersection with the x-axis and y-axis. Please enter your answer as a set of coordi      Log On


   



Question 993481: Given the function
y = ( x+3 ) ( x^2+3 x−3 )
find the coordinates of the points of intersection with the x-axis and y-axis.
Please enter your answer as a set of coordinate pairs, where a single coordinate pair (a, b)
constants should all be given exactly, using the sqrt function and fractions as necessary
THANK YOU

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
y=%28+x%2B3+%29+%28+x%5E2%2B3x-3+%29
intersection with the x-axis occurs where y=0
and
intersection with the y-axis occurs where x=0
so set y=0 and find intersection with the x-axis
0=%28+x%2B3+%29+%28+x%5E2%2B3x-3+%29...will be true for %28+x%2B3+%29=0 or %28+x%5E2%2B3x-3+%29=0, or both
if %28+x%2B3+%29=0=>highlight%28x=-3%29
%28+x%5E2%2B3x-3+%29=0...use quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-3+%2B-+sqrt%28+3%5E2-4%2A1%2A%28-3%29+%29%29%2F%282%2A1%29+
x+=+%28-3+%2B-+sqrt%28+9%2B12+%29%29%2F2+
x+=+%28-3+%2B-+sqrt%28+21+%29%29%2F2+
solutions: exact solutions
highlight%28x+=+%28-3+%2B+sqrt%28+21+%29%29%2F2+%29
or
highlight%28x+=+%28-3+-+sqrt%28+21+%29%29%2F2%29+
approximate solutions:
x+=+%28-3+%2B+sqrt%28+21+%29%29%2F2+
x+=+%28-3+%2B+4.6%29%2F2+
x+=+%281.6%29%2F2+
highlight%28x+=0.8+%29
or
x+=+%28-3+-+sqrt%28+21+%29%29%2F2+
x+=+%28-3+-+4.6%29%2F2+
x+=+%28-7.6%29%2F2+
highlight%28x+=-3.8%29+

so, ordered pairs are:
(-3+,0)
(%28-3+%2B+sqrt%28+21+%29%29%2F2+,0)
(%28-3+-+sqrt%28+21+%29%29%2F2+,0)
or
(-3+,0)
(0.8+,0)
(-3.8+,0)

now find y-intercept:

the y-axis occurs where x=0, so set x=0
y=%28+0%2B3+%29+%28+0%5E2%2B3%2A0-3+%29
y=%28+3+%29+%28+-3+%29
highlight%28y=+-9%29
ordered pair is:
(0+,-9)

see it on the graph:
+graph%28+600%2C+600%2C+-15%2C+15%2C+-15%2C+15%2C%28+x%2B3+%29+%28+x%5E2%2B3x-3+%29%29+