820 Вправа 820Алгебра 8 клас Тарасенкова 2025 · § 20 · стор. 244

820. Побудуйте графік функції:

1) ОДЗ: ${\displaystyle x-2\ne 0}$; ${\displaystyle x\ne 2}$;

${\displaystyle x^2-5x+6=}$${\displaystyle 0}$;

${\displaystyle x_1+x_2=}$${\displaystyle 5}$; ${\displaystyle x_1\cdot x_2=}$${\displaystyle 6}$;

${\displaystyle x_1=}$${\displaystyle 2}$; ${\displaystyle x_2=}$${\displaystyle 3}$;

${\displaystyle x^2-5x+6=}$${\displaystyle (x-2)(x-3)}$;

${\displaystyle y=}$${\displaystyle \frac{x^2-5x+6}{x-2}=}$${\displaystyle \frac{\cancel{\left(x-2\right)}(x-3)}{\cancel{\left(x-2\right)}}=}$${\displaystyle x-3}$;

виколота точка: ${\displaystyle x=}$${\displaystyle 2}$, ${\displaystyle y=}$${\displaystyle 2-3=}$${\displaystyle -1}$, ${\displaystyle \left(2;-1\right)}$;

${\displaystyle y=}$${\displaystyle x-3}$:

2) ОДЗ: ${\displaystyle x+2\ne 0}$; ${\displaystyle x\ne -2}$;

${\displaystyle 2x^2+3x-2=}$${\displaystyle 0}$;

${\displaystyle D=}$${\displaystyle 3^2-4\cdot 2\cdot (-2)=}$${\displaystyle 9+16=}$${\displaystyle 25}$;

${\displaystyle x_{1,2}=}$${\displaystyle \frac{-3\pm \sqrt{25}}{2\cdot 2}=}$${\displaystyle \frac{-3\pm 5}{4}}$;

${\displaystyle x_1=}$${\displaystyle \frac{-3+5}{4}=}$${\displaystyle \frac{2}{4}=}$${\displaystyle 0,5}$;

${\displaystyle x_2=}$${\displaystyle \frac{-3-5}{4}=}$${\displaystyle -2}$;

${\displaystyle 2x^2+3x-2=}$${\displaystyle 2(x-\frac{1}{2})(x+2)=}$${\displaystyle (2x-1)(x+2)}$;

${\displaystyle y=}$${\displaystyle \frac{2x^2+3x-2}{x+2}=}$${\displaystyle \frac{(2x-1)\cancel{\left(x+2\right)}}{\cancel{\left(x+2\right)}}=}$${\displaystyle 2x-1}$;

виколота точка: ${\displaystyle x=}$${\displaystyle -2}$, ${\displaystyle y=}$${\displaystyle 2\cdot (-2)-1=}$${\displaystyle -5}$, ${\displaystyle \left(-2;-5\right)}$;

${\displaystyle y=}$${\displaystyle 2x-1}$: