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Popular >

f(t)=6t^2+500t+8000

Solution

f (t) = 6 t^{2} + 500 t + 8000

Solution

Domain : - \infty < t < \infty

Range : f (t) \geq - \frac{7250}{3}

X Intercepts : (\frac{5 ( 145 - 25 )}{3}, 0), (- \frac{5 ( 25 + 145 )}{3}, 0), Y Intercepts : (0, 8000)

Vertex : Minimum (- \frac{125}{3}, - \frac{7250}{3})

Inverse : \frac{- 500 + 24 t + 58000}{12}, \frac{- 500 - 24 t + 58000}{12}

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [- \frac{7250}{3}, \infty)

Solution steps

Domain of

6 t^{2} + 500 t + 8000 : - \infty < t < \infty

Range of

6 t^{2} + 500 t + 8000 : f (t) \geq - \frac{7250}{3}

Axis interception points of

6 t^{2} + 500 t + 8000 :

X Intercepts

: (\frac{5 ( 145 - 25 )}{3}, 0), (- \frac{5 ( 25 + 145 )}{3}, 0),

Y Intercepts

: (0, 8000)

Vertex of

6 t^{2} + 500 t + 8000 :

Minimum

(- \frac{125}{3}, - \frac{7250}{3})

Inverse of

6 t^{2} + 500 t + 8000 : \frac{- 500 + 24 t + 58000}{12}, \frac{- 500 - 24 t + 58000}{12}

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