Whakaoti i te h(t)=-16t^2+96t+2

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

Tauwehe

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

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.

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

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.

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

Pūrua 96.

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

Whakareatia -4 ki te -16.

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

Whakareatia 64 ki te 2.

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

Tāpiri 9216 ki te 128.

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

Tuhia te pūtakerua o te 9344.

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

Whakareatia 2 ki te -16.

$$t=\frac{-96±8\sqrt{146}}{-32}$$

Nā, me whakaoti te whārite t=\frac{-96±8\sqrt{146}}{-32} ina he tāpiri te ±. Tāpiri -96 ki te 8\sqrt{146}.

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

Whakawehe -96+8\sqrt{146} ki te -32.

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

Nā, me whakaoti te whārite t=\frac{-96±8\sqrt{146}}{-32} ina he tango te ±. Tango 8\sqrt{146} mai i -96.

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

Whakawehe -96-8\sqrt{146} ki te -32.

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

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 3-\frac{\sqrt{146}}{4} mō te x_{1} me te 3+\frac{\sqrt{146}}{4} mō te x_{2}.

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

Aromātai

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