Question
Find the indicated functions.Find the function $f(x)=a x^{2}+b x+c,$ if $f(1)=3$ $f(-2)=15,$ and $f(3)=5$
Step 1
Step 1: We are given three equations from the function $f(x)=ax^{2}+bx+c$: $$f(1)=a(1)^{2}+b(1)+c=3$$ $$f(-2)=a(-2)^{2}+b(-2)+c=15$$ $$f(3)=a(3)^{2}+b(3)+c=5$$ which simplifies to: $$a+b+c=3$$ $$4a-2b+c=15$$ $$9a+3b+c=5$$ Show more…
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