h(t)=-16t^2+96t+2 eching

$$h ( t ) = - 16 t ^ { 2 } + 96 t + 2$$

Omil

$$-16\left(t-\left(-\frac{\sqrt{146}}{4}+3\right)\right)\left(t-\left(\frac{\sqrt{146}}{4}+3\right)\right)$$

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.

$$-16t^{2}+96t+2=0$$

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.

$$t=\frac{-96±\sqrt{96^{2}-4\left(-16\right)\times 2}}{2\left(-16\right)}$$

96 kvadratini chiqarish.

$$t=\frac{-96±\sqrt{9216-4\left(-16\right)\times 2}}{2\left(-16\right)}$$

-4 ni -16 marotabaga ko'paytirish.

$$t=\frac{-96±\sqrt{9216+64\times 2}}{2\left(-16\right)}$$

64 ni 2 marotabaga ko'paytirish.

$$t=\frac{-96±\sqrt{9216+128}}{2\left(-16\right)}$$

9216 ni 128 ga qo'shish.

$$t=\frac{-96±\sqrt{9344}}{2\left(-16\right)}$$

9344 ning kvadrat ildizini chiqarish.

$$t=\frac{-96±8\sqrt{146}}{2\left(-16\right)}$$

2 ni -16 marotabaga ko'paytirish.

$$t=\frac{-96±8\sqrt{146}}{-32}$$

t=\frac{-96±8\sqrt{146}}{-32} tenglamasini yeching, bunda ± musbat. -96 ni 8\sqrt{146} ga qo'shish.

$$t=\frac{8\sqrt{146}-96}{-32}$$

-96+8\sqrt{146} ni -32 ga bo'lish.

$$t=-\frac{\sqrt{146}}{4}+3$$

t=\frac{-96±8\sqrt{146}}{-32} tenglamasini yeching, bunda ± manfiy. -96 dan 8\sqrt{146} ni ayirish.

$$t=\frac{-8\sqrt{146}-96}{-32}$$

-96-8\sqrt{146} ni -32 ga bo'lish.

$$t=\frac{\sqrt{146}}{4}+3$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun 3-\frac{\sqrt{146}}{4} ga va x_{2} uchun 3+\frac{\sqrt{146}}{4} ga bo‘ling.

$$-16t^{2}+96t+2=-16\left(t-\left(-\frac{\sqrt{146}}{4}+3\right)\right)\left(t-\left(\frac{\sqrt{146}}{4}+3\right)\right)$$

Baholash

$$2+96t-16t^{2}$$