Question

область значень y=x2-5x

Answer 1

$y=x^2-5x, \ x^2-2cdotfrac{5}{2}x+(frac{5}{2})^2-(frac{5}{2})^2=y, \ (x-frac{5}{2})^2=y+frac{25}{4}, \ x-frac{5}{2}=sqrt{y+frac{25}{4}}, \ x=sqrt{y+frac{25}{4}}+frac{5}{2}, \ y+frac{25}{4}geq0, \ ygeq-frac{25}{4}, \ E_y=[-frac{25}{4};+infty).$

II.
$y=x^2-5x, \ a=1 textgreater 0, b=-5, c=0, \ x_0=-frac{b}{2a}=-frac{-5}{2cdot1}=frac{5}{2}, \ y_0=x_0^2-5x_0=(frac{5}{2})^2-5cdotfrac{5}{2}=frac{25}{4}-frac{25}{2}=-frac{25}{4}, \ {y_0=-frac{D}{4a}=frac{4ac-b^2}{4a}=frac{4cdot1cdot0-5^2}{4cdot1}=frac{0-25}{4}=-frac{25}{4}} \ ygeq y_0, ygeq-frac{25}{4}.$