f(x)=-4x^2+16x+2 eching

$$f ( x ) = - 4 x ^ { 2 } + 16 x + 2$$

Omil

$$-4\left(x-\left(-\frac{3\sqrt{2}}{2}+2\right)\right)\left(x-\left(\frac{3\sqrt{2}}{2}+2\right)\right)$$

Kvadrat tenglamalaridan foydalanish qoidalari

Kvadrat koʻp tenglama bu orqali hisoblanadi: ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), bu yerda x_{1} va x_{2} ax^{2}+bx+c=0 kvadrat tenglamaning yechimlari.

$$-4x^{2}+16x+2=0$$

ax^{2}+bx+c=0 shaklidagi barcha tenglamalarni kvadrat formulasi bilan yechish mumkin: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Kvadrat formula ikki yechmni taqdim qiladi, biri ± qo'shish bo'lganda, va ikkinchisi ayiruv bo'lganda.

$$x=\frac{-16±\sqrt{16^{2}-4\left(-4\right)\times 2}}{2\left(-4\right)}$$

16 kvadratini chiqarish.

$$x=\frac{-16±\sqrt{256-4\left(-4\right)\times 2}}{2\left(-4\right)}$$

-4 ni -4 marotabaga ko'paytirish.

$$x=\frac{-16±\sqrt{256+16\times 2}}{2\left(-4\right)}$$

16 ni 2 marotabaga ko'paytirish.

$$x=\frac{-16±\sqrt{256+32}}{2\left(-4\right)}$$

256 ni 32 ga qo'shish.

$$x=\frac{-16±\sqrt{288}}{2\left(-4\right)}$$

288 ning kvadrat ildizini chiqarish.

$$x=\frac{-16±12\sqrt{2}}{2\left(-4\right)}$$

2 ni -4 marotabaga ko'paytirish.

$$x=\frac{-16±12\sqrt{2}}{-8}$$

x=\frac{-16±12\sqrt{2}}{-8} tenglamasini yeching, bunda ± musbat. -16 ni 12\sqrt{2} ga qo'shish.

$$x=\frac{12\sqrt{2}-16}{-8}$$

-16+12\sqrt{2} ni -8 ga bo'lish.

$$x=-\frac{3\sqrt{2}}{2}+2$$

x=\frac{-16±12\sqrt{2}}{-8} tenglamasini yeching, bunda ± manfiy. -16 dan 12\sqrt{2} ni ayirish.

$$x=\frac{-12\sqrt{2}-16}{-8}$$

-16-12\sqrt{2} ni -8 ga bo'lish.

$$x=\frac{3\sqrt{2}}{2}+2$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun 2-\frac{3\sqrt{2}}{2} ga va x_{2} uchun 2+\frac{3\sqrt{2}}{2} ga bo‘ling.

$$-4x^{2}+16x+2=-4\left(x-\left(-\frac{3\sqrt{2}}{2}+2\right)\right)\left(x-\left(\frac{3\sqrt{2}}{2}+2\right)\right)$$

Baholash

$$2+16x-4x^{2}$$