Whakaoti i te h(t)=-16t^2+92t+20

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

Tauwehe

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

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Ka taea te huamaha pūrua te tauwehe mā te whakamahi i te huringa ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), ina ko x_{1} me x_{2} ngā otinga o te whārite pūrua ax^{2}+bx+c=0.

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

Ko ngā whārite katoa o te āhua ax^{2}+bx+c=0 ka taea te whakaoti mā te whakamahi i te tikanga tātai pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. E rua ngā otinga ka puta i te tikanga tātai pūrua, ko tētahi ina he tāpiri a ±, ā, ko tētahi ina he tango.

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

Pūrua 92.

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

Whakareatia -4 ki te -16.

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

Whakareatia 64 ki te 20.

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

Tāpiri 8464 ki te 1280.

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

Tuhia te pūtakerua o te 9744.

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

Whakareatia 2 ki te -16.

$$t=\frac{-92±4\sqrt{609}}{-32}$$

Nā, me whakaoti te whārite t=\frac{-92±4\sqrt{609}}{-32} ina he tāpiri te ±. Tāpiri -92 ki te 4\sqrt{609}.

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

Whakawehe -92+4\sqrt{609} ki te -32.

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

Nā, me whakaoti te whārite t=\frac{-92±4\sqrt{609}}{-32} ina he tango te ±. Tango 4\sqrt{609} mai i -92.

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

Whakawehe -92-4\sqrt{609} ki te -32.

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

Tauwehea te kīanga taketake mā te whakamahi i te ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Me whakakapi te \frac{23-\sqrt{609}}{8} mō te x_{1} me te \frac{23+\sqrt{609}}{8} mō te x_{2}.

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

Aromātai

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