Question

Quadratic function h can be used to model the height in feet of a rocket from the ground
t seconds after it was launched. The graph of the function is shown.

Answer 1

Answer:

t = -b 2a = -120/(-32) = 3.75 The height of the rocket is a maximum 3.75 seconds after its launch. To find the height we only need to plug into the model: s(3.75) = -16(3.752) + 120(3.75) + 80 = 305 The maximum height of the rocket is 305 feet.

Step-by-step explanation:

Answer 2

The maximum value of graph of function is (3.75,225).

How to build the equation and find value of x-axis ?

We consider, the equation is y=a(x-0)(x-7.5)

Now, when x=6 and y = 144

144=6a(-1.5)

⇒a= - 144/9

⇒a= -16

Now,  y= -16(x-0)(x-7.5)

⇒ y= -16$x^{2}$+120x

∴ x = -b/2a = -120/(-32) = 3.75

How to find y co-ordinate ?

When x=3.75, then the value of y is maximum.

∴ $y_{max}$ = $-16(3.75)^{2}+120*3.75$

          = 225

Hence, the maximum value of y is 225.

So, the required co-ordinate is (3.75,225).

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