Fill in quadratic function table.

Question

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}

Answer 1

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 $0$.

Answer 2

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?

Answer 3

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 $x=-1$

$y=-\frac{2}{3}(-1-1)(-1+3)$.

$y=-\frac{2}{3}(-2)(2)$.

$y=\frac{8}{3}$.