h(t)=-16t^2+416t+32 eching

$$h ( t ) = - 16 t ^ { 2 } + 416 t + 32$$

Omil

$$-16\left(t-\left(13-3\sqrt{19}\right)\right)\left(t-\left(3\sqrt{19}+13\right)\right)$$

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.

$$-16t^{2}+416t+32=0$$

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.

$$t=\frac{-416±\sqrt{416^{2}-4\left(-16\right)\times 32}}{2\left(-16\right)}$$

416 kvadratini chiqarish.

$$t=\frac{-416±\sqrt{173056-4\left(-16\right)\times 32}}{2\left(-16\right)}$$

-4 ni -16 marotabaga ko'paytirish.

$$t=\frac{-416±\sqrt{173056+64\times 32}}{2\left(-16\right)}$$

64 ni 32 marotabaga ko'paytirish.

$$t=\frac{-416±\sqrt{173056+2048}}{2\left(-16\right)}$$

173056 ni 2048 ga qo'shish.

$$t=\frac{-416±\sqrt{175104}}{2\left(-16\right)}$$

175104 ning kvadrat ildizini chiqarish.

$$t=\frac{-416±96\sqrt{19}}{2\left(-16\right)}$$

2 ni -16 marotabaga ko'paytirish.

$$t=\frac{-416±96\sqrt{19}}{-32}$$

t=\frac{-416±96\sqrt{19}}{-32} tenglamasini yeching, bunda ± musbat. -416 ni 96\sqrt{19} ga qo'shish.

$$t=\frac{96\sqrt{19}-416}{-32}$$

-416+96\sqrt{19} ni -32 ga bo'lish.

$$t=13-3\sqrt{19}$$

t=\frac{-416±96\sqrt{19}}{-32} tenglamasini yeching, bunda ± manfiy. -416 dan 96\sqrt{19} ni ayirish.

$$t=\frac{-96\sqrt{19}-416}{-32}$$

-416-96\sqrt{19} ni -32 ga bo'lish.

$$t=3\sqrt{19}+13$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun 13-3\sqrt{19} ga va x_{2} uchun 13+3\sqrt{19} ga bo‘ling.

$$-16t^{2}+416t+32=-16\left(t-\left(13-3\sqrt{19}\right)\right)\left(t-\left(3\sqrt{19}+13\right)\right)$$

Baholash

$$32+416t-16t^{2}$$