Question

построить график функции y=-2x^+5|x|-2

Answer 1

$y=-2x^2+5|x|-2=-2(x^2-frac{5}{2}|x|+1)=\=-2(x^2-2cdotfrac{5}{4}|x|+frac{25}{16}-frac{25}{16}+1)=-2((|x|-frac{5}{4})^2-frac{9}{16})=\=-2(|x|-frac{5}{4})^2+frac{9}{8}, \ y= left { {{-2(x-frac{5}{4})^2+frac{9}{8}, x geq 0} atop {-2(x+frac{5}{4})^2+frac{9}{8}, x textless 0.}} right.$