SOLUTION: A quadratic function has equation f(x)=x2-x-6. Determine the x-intercepts for each function. a) y=f(2x) b) y=f(1/3x) c) y=f(-3x)

Algebra ->  Functions -> SOLUTION: A quadratic function has equation f(x)=x2-x-6. Determine the x-intercepts for each function. a) y=f(2x) b) y=f(1/3x) c) y=f(-3x)      Log On


   

Question 949902: A quadratic function has equation f(x)=x2-x-6. Determine the x-intercepts for each function.
a) y=f(2x)
b) y=f(1/3x)
c) y=f(-3x)
Answer by MathLover1(20855) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29+=+x%5E2+-x+-6...factor completely
f%28x%29+=+x%5E2%2B2x+-3x+-6
f%28x%29+=+%28x%5E2%2B2x%29+-%283x+%2B6%29
f%28x%29+=+x%28x%2B2%29+-3%28x+%2B2%29
f%28x%29+=+%28x+-3%29%28x+%2B+2%29
x intercepts for this are:
x+-3+=+0=> x+=+3
and x+%2B+2+=+0=>x+=+-2
To find the intercepts for each of the following
a) y=f%282x%29
b) y=f%281%2F3x%29
c) y=f%28-3x%29
simply substitute the new x values
a)
2x+=+3 or highlight%28x+=+3%2F2%29 and 2x+=+-2 or highlight%28x+=+-1%29
b)
%281%2F3%29x+=+3 or highlight%28x+=+9%29 and %281%2F3%29x+=+-2 or highlight%28x+=-6%29
c)
-3x+=+3 or highlight%28x+=+-1%29 and -3x+=+-2 or highlight%28x+=+2%2F3%29

you can also do it this way:
a)
y=f%282x%29=%282x%29%5E2-2x-6
y=+4x%5E2-2x-6
set y to zero to find the x-intercepts
0=+4x%5E2-2x-6...........both sides divide by 2
0=+2x%5E2-x-3...........factor
2x%5E2%2B2x-3x-3=0
%282x%5E2%2B2x%29-%283x%2B3%29=0
2x%28x%2B1%29-3%28x%2B1%29=0
%28x%2B1%29+%282x-3%29=0
if %28x%2B1%29+=0+=> x=-1
if %282x-3%29=0=>x=3%2F2
the x-intercepts are x=-1 and x=3%2F2+
same way you can do b) and c)