SOLUTION: How do I proceed with this problem? Find a, b, and c such that the graph of y= ax^2 + (b times the square root of x) + c goes through the points (0,3), (1,-1/2), and (4,3). Any he

Algebra ->  Rational-functions -> SOLUTION: How do I proceed with this problem? Find a, b, and c such that the graph of y= ax^2 + (b times the square root of x) + c goes through the points (0,3), (1,-1/2), and (4,3). Any he      Log On


   

Question 79630: How do I proceed with this problem?
Find a, b, and c such that the graph of y= ax^2 + (b times the square root of x) + c goes through the points (0,3), (1,-1/2), and (4,3). Any help would be much appreciated.
Answer by Edwin McCravy(20065) About Me  (Show Source):
You can put this solution on YOUR website!

How do I proceed with this problem?
Find a, b, and c such that the graph of
y= ax^2 + (b times the square root of x) + c 
goes through the points (0,3), (1,-1/2), and (4,3).
Any help would be much appreciated

y+=+ax%5E2+%2B+b%2Asqrt%28x%29+%2B+c

Plug in each point.

Plugging in (x,y) = (0,3)

3+=+a%280%29%5E2+%2B+b%2Asqrt%280%29+%2B+c

which simplifies to

3+=+c

Plugging in (x,y) = (1,-1/2)

-1%2F2+=+a%281%29%5E2+%2B+b%2Asqrt%281%29+%2B+c

which simplifies to

-1%2F2+=+a%2Bb%2Bc

Plugging in (x,y) = (4,3)

3+=+a%284%29%5E2+%2B+b%2Asqrt%284%29+%2B+c

which simplifies to

3+=+16a+%2B+2b+%2B+c
 
So we have the system of equations:

3+=+c
-1%2F2+=+a%2Bb%2Bc
3+=+16a+%2B+2b+%2B+c

Can you now find a and b?  Start out
by substituting 3 for c.  If you can't
find them post again asking how.

Answers: a = 1/2, b = -4, c = 3 

so the equation is

f%28x%29+=+%281%2F2%29x%5E2+-4%2Asqrt%28x%29%2B3

and it's graph is

graph%28300%2C300%2C-2%2C5%2C-2%2C5%2C+%281%2F2%29x%5E2+-4%2Asqrt%28x%29%2B3%29

Edwin