Réitigh h(t)=-16t^2+96t+2

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

Fachtóirigh

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

Céimeanna ag Baint Úsáid as an bhFoirmle Chearnach

Is féidir an trasfhoirmiú ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) a úsáid chun luach iltéarmach cearnach a fhachtóiriú, nuair is réitigh iad x_{1} agus x_{2} ar an gcothromóid chearnach ax^{2}+bx+c=0.

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

Is féidir gach cothromóid san fhoirm ax^{2}+bx+c=0 a réiteach ag baint úsáid as an bhfoirmle chearnach : \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Tugann an fhoirmle chearnach dhá réiteach, ceann amháin nuair is suimiú é ± agus ceann eile nuair is dealú é.

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

Cearnóg 96.

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

Méadaigh -4 faoi -16.

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

Méadaigh 64 faoi 2.

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

Suimigh 9216 le 128?

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

Tóg fréamh chearnach 9344.

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

Méadaigh 2 faoi -16.

$$t=\frac{-96±8\sqrt{146}}{-32}$$

Réitigh an chothromóid t=\frac{-96±8\sqrt{146}}{-32} nuair is ionann ± agus plus. Suimigh -96 le 8\sqrt{146}?

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

Roinn -96+8\sqrt{146} faoi -32.

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

Réitigh an chothromóid t=\frac{-96±8\sqrt{146}}{-32} nuair is ionann ± agus míneas. Dealaigh 8\sqrt{146} ó -96.

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

Roinn -96-8\sqrt{146} faoi -32.

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

Úsáid ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) chun an slonn bunaidh a fhachtóiriú. Cuir 3-\frac{\sqrt{146}}{4} in ionad x_{1} agus 3+\frac{\sqrt{146}}{4} in ionad x_{2}.

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

Luacháil

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