Fill in quadratic function table.
How would you fill in this quadratic table?
\begin{array}{|c|c|}\hline x& y \\ \hline -3& 0 \\ \hline -2& 2 \\ \hline -1& ? \\ \hline 0& ? \\ \hline 1& 0 \\ \hline \end{array}
$\endgroup$3 Answers
$\begingroup$Guide:
- Step $1$: Find the quadratic equation that passeas through $(-3,0), (-2,2), (1,0)$
- Step $2$: Evaluate that quadratic equation formula that you have foundat $-1$ and $0$.
Hint:
This is a quadratic equation, meaning it has at most 2 roots. You have been given some points, two of which give you the roots, $b,c$ of the quadratic. Using this, you can construct the quadratic $y=\alpha(x-b)(x-c)$. Then the third point will allow you to determine $\alpha$.
Do you think you can do it from here?
$\endgroup$ $\begingroup$This is a quadratic equation, meaning it has at most 2 roots. The quadratic $y=\alpha(x-1)(x+3)$.
put $x=-2 , y=2$
$2=\alpha(-3)(1)$
$2=-3\alpha$
$-2/3=\alpha$
$y=-\frac{2}{3}(x-1)(x+3)$.
for $x=0$
$y=-\frac{2}{3}(0-1)(0+3)$.
$y=2$
for $x=-1$
$y=-\frac{2}{3}(-1-1)(-1+3)$.
$y=-\frac{2}{3}(-2)(2)$.
$y=\frac{8}{3}$.
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