h(t)=-16t^2+92t+20 eching

$$h ( t ) = - 16 t ^ { 2 } + 92 t + 20$$

Omil

$$-16\left(t-\frac{23-\sqrt{609}}{8}\right)\left(t-\frac{\sqrt{609}+23}{8}\right)$$

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.

$$-16t^{2}+92t+20=0$$

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.

$$t=\frac{-92±\sqrt{92^{2}-4\left(-16\right)\times 20}}{2\left(-16\right)}$$

92 kvadratini chiqarish.

$$t=\frac{-92±\sqrt{8464-4\left(-16\right)\times 20}}{2\left(-16\right)}$$

-4 ni -16 marotabaga ko'paytirish.

$$t=\frac{-92±\sqrt{8464+64\times 20}}{2\left(-16\right)}$$

64 ni 20 marotabaga ko'paytirish.

$$t=\frac{-92±\sqrt{8464+1280}}{2\left(-16\right)}$$

8464 ni 1280 ga qo'shish.

$$t=\frac{-92±\sqrt{9744}}{2\left(-16\right)}$$

9744 ning kvadrat ildizini chiqarish.

$$t=\frac{-92±4\sqrt{609}}{2\left(-16\right)}$$

2 ni -16 marotabaga ko'paytirish.

$$t=\frac{-92±4\sqrt{609}}{-32}$$

t=\frac{-92±4\sqrt{609}}{-32} tenglamasini yeching, bunda ± musbat. -92 ni 4\sqrt{609} ga qo'shish.

$$t=\frac{4\sqrt{609}-92}{-32}$$

-92+4\sqrt{609} ni -32 ga bo'lish.

$$t=\frac{23-\sqrt{609}}{8}$$

t=\frac{-92±4\sqrt{609}}{-32} tenglamasini yeching, bunda ± manfiy. -92 dan 4\sqrt{609} ni ayirish.

$$t=\frac{-4\sqrt{609}-92}{-32}$$

-92-4\sqrt{609} ni -32 ga bo'lish.

$$t=\frac{\sqrt{609}+23}{8}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{23-\sqrt{609}}{8} ga va x_{2} uchun \frac{23+\sqrt{609}}{8} ga bo‘ling.

$$-16t^{2}+92t+20=-16\left(t-\frac{23-\sqrt{609}}{8}\right)\left(t-\frac{\sqrt{609}+23}{8}\right)$$

Baholash

$$20+92t-16t^{2}$$