Question

PLEASE SOMEONE HELP ME. Use the given values to write a quadratic equation of the form f(x)=ax^2+bx+c:

a) f(1)=3. f(2)=5. f(3)=9
b) f(0)=1. f(2)=-1 and f(-2)=7
c) Vertex (2, -3) passing through the point (4, -1)
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Answer 1

C)

`\bf ~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{`

`\bf \stackrel{vertex}{(2,-3)}~~ \begin{cases} h=2\\ k=-3 \end{cases}\implies y = a(x-2)^2-3 \\\\\\ \stackrel{passes~through}{(4,-1)}~~ \begin{cases} x=4\\ y=-1 \end{cases}\implies -1=a(4-2)^2-3\implies 2=a(4-2)^2 \\\\\\ 2=a(2)^2\implies 2=4a\implies \cfrac{2}{4}=a\implies \cfrac{1}{2}=a \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill y=\cfrac{1}{2}(x-2)^2-3~\hfill`