Question 79630
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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^2 + b*sqrt(x) + c}}}

Plug in each point.

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

{{{3 = a(0)^2 + b*sqrt(0) + c}}}

which simplifies to

{{{3 = c}}}

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

{{{-1/2 = a(1)^2 + b*sqrt(1) + c}}}

which simplifies to

{{{-1/2 = a+b+c}}}

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

{{{3 = a(4)^2 + b*sqrt(4) + c}}}

which simplifies to

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

{{{3 = c}}}
{{{-1/2 = a+b+c}}}
{{{3 = 16a + 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(x) = (1/2)x^2 -4*sqrt(x)+3}}}

and it's graph is

{{{graph(300,300,-2,5,-2,5, (1/2)x^2 -4*sqrt(x)+3)}}}

Edwin</pre>