Find the quadratic equation that fits the following.
{(4,-152),(-3,-40),(-2,14)}

Question

Find the quadratic equation that fits the following.
{(4,-152),(-3,-40),(-2,14)}

amistre64 · Answer

id cheat and use a rref coeff matrix

amistre64 · Answer

i was gonna see about verifying elias results ;)

amistre64 · Answer

http://www.wolframalpha.com/input/?i=rref%7B%7B4%5E2%2C4%2C1%2C-152%7D%2C%7B%28-3%29%5E2%2C-3%2C1%2C-40%7D%2C%7B%28-2%29%5E2%2C-2%2C1%2C14%7D%7D it aint purty, but the rightmost column is the coefficient vector of your quadratic

anonymous · Answer

Let
$$f(x)-a x^2+b x+c \
f(4)= 16 a+4 b+c=-152\
f(-3)=9 a-3 b+c =-40\
f(-2)=4 a-2 b+c=14
$$
Solve the three equations and you get
$$
 \left\{a=-\frac{35}{3},b=-\frac{13}{3},c=52\right\}
$$
Hence
$$
f(x)= -\frac{35 x^2}{3}-\frac{13
   x}{3}+52
$$

amistre64 · Answer

yep, that verifies it :)