SOLUTION: Given the function f(x)=2x^2+3x-1, find the value(s) of k so that f(k+2)=-2. Express your answer(s) as an integer or decimal. Do not use fractions. Thanks for your help.

Algebra ->  Equations -> SOLUTION: Given the function f(x)=2x^2+3x-1, find the value(s) of k so that f(k+2)=-2. Express your answer(s) as an integer or decimal. Do not use fractions. Thanks for your help.      Log On


   

Question 946196: Given the function f(x)=2x^2+3x-1, find the value(s) of k so that f(k+2)=-2. Express your answer(s) as an integer or decimal. Do not use fractions. Thanks for your help.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

f%28x%29=2x%5E2%2B3x-1,
the value(s) of k so that f%28k%2B2%29=-2 will be:
-2=2%28k%2B2%29%5E2%2B3%28k%2B2%29-1
-2=2%28k%5E2%2B4k%2B4%29%2B3%28k%2B2%29-1
-2=2k%5E2%2B8k%2B8%2B3k%2B6-1
-2=2k%5E2%2B11k%2B13
0=2k%5E2%2B11k%2B13%2B2
2k%5E2%2B11k%2B15=0
2k%5E2%2B5k%2B6k%2B15+=+0
%282k%5E2%2B5k%29%2B%286k%2B15%29+=+0
k%282k%2B5%29%2B3%282k%2B5%29+=+0
%28k%2B3%29%282k%2B5%29+=+0
solutions:
if %28k%2B3%29+=+0=> k=-3
if %282k%2B5%29+=+0=>2k=-5=>k=-5%2F2