Mathematics, 04.07.2019 02:00 homeschool0123
For the function, the vertex of the function's graph is given. find the unknown coefficients. y=x^2+bx+c ; (-2,4)
Answers: 1
![\bf \textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{+b}x\stackrel{\stackrel{c}{\downarrow }}{+c} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right)~~=~~(-2,4) \\\\[-0.35em] ~\dotfill\\\\ -\cfrac{b}{2a}=-2\implies -\cfrac{b}{2(1)}=-2\implies -b=-4\implies \boxed{b=4} \\\\[-0.35em] ~\dotfill](/tpl/images/0048/5578/2acfd.png)
![\bf c-\cfrac{ b^2}{4 a}=4\implies c-\cfrac{\boxed{4}^2}{4(1)}=4\implies c-\cfrac{16}{4}=4 \\\\\\ c-4=4\implies \boxed{c=8} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill y=x^2+4x+8~\hfill](/tpl/images/0048/5578/e253b.png)
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For the function, the vertex of the function's graph is given. find the unknown coefficients. y=x^2+...
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