Réitigh h(t)=-16t^2+92t+20

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

Fachtóirigh

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

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.

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

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.

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

Cearnóg 92.

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

Méadaigh -4 faoi -16.

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

Méadaigh 64 faoi 20.

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

Suimigh 8464 le 1280?

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

Tóg fréamh chearnach 9744.

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

Méadaigh 2 faoi -16.

$$t=\frac{-92±4\sqrt{609}}{-32}$$

Réitigh an chothromóid t=\frac{-92±4\sqrt{609}}{-32} nuair is ionann ± agus plus. Suimigh -92 le 4\sqrt{609}?

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

Roinn -92+4\sqrt{609} faoi -32.

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

Réitigh an chothromóid t=\frac{-92±4\sqrt{609}}{-32} nuair is ionann ± agus míneas. Dealaigh 4\sqrt{609} ó -92.

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

Roinn -92-4\sqrt{609} faoi -32.

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

Úsáid ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) chun an slonn bunaidh a fhachtóiriú. Cuir \frac{23-\sqrt{609}}{8} in ionad x_{1} agus \frac{23+\sqrt{609}}{8} in ionad x_{2}.

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

Luacháil

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