Whakaoti i te h(t)=-16t^2+416t+32

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

Tauwehe

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

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.

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

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.

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

Pūrua 416.

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

Whakareatia -4 ki te -16.

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

Whakareatia 64 ki te 32.

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

Tāpiri 173056 ki te 2048.

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

Tuhia te pūtakerua o te 175104.

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

Whakareatia 2 ki te -16.

$$t=\frac{-416±96\sqrt{19}}{-32}$$

Nā, me whakaoti te whārite t=\frac{-416±96\sqrt{19}}{-32} ina he tāpiri te ±. Tāpiri -416 ki te 96\sqrt{19}.

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

Whakawehe -416+96\sqrt{19} ki te -32.

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

Nā, me whakaoti te whārite t=\frac{-416±96\sqrt{19}}{-32} ina he tango te ±. Tango 96\sqrt{19} mai i -416.

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

Whakawehe -416-96\sqrt{19} ki te -32.

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

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 13-3\sqrt{19} mō te x_{1} me te 13+3\sqrt{19} mō te x_{2}.

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

Aromātai

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