Question

What is the vortex of the graph of the quadratic function%7B2%7D%20%20%2B%202x%20-%202" id="TexFormula1" title="f(x) = x {}^{2} + 2x - 2" alt="f(x) = x {}^{2} + 2x - 2" align="absmiddle" class="latex-formula">

Answer 1

$\bf \textit{vertex of a vertical parabola, using coefficients} \\\\ \stackrel{f(x)}{y}=\stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{+2}x\stackrel{\stackrel{c}{\downarrow }}{-2} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left( -\cfrac{2}{2(1)}~~,~~-2-\cfrac{2^2}{4(1)} \right)\implies \left( -1~~,~~-2-1 \right)\implies (-1~,-3)$