Question

Explain in detail how to find the vertex:  y=-2x^2 + 2x + 3

Answer 1

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

$\bf \left(-\cfrac{2}{2(-2)}~~,~~3-\cfrac{2^2}{4(-2)} \right)\implies \left( \cfrac{1}{2}~~,~~3+\cfrac{4}{8} \right)\implies \left(\cfrac{1}{2}~~,~~\cfrac{28}{8} \right) \\\\\\ \left(\cfrac{1}{2}~~,~~\cfrac{7}{2} \right)\implies \left(\frac{1}{2}~,~3\frac{1}{2} \right)$