Answered

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A bottle rocket is launched straight up. Its height in feet (y) above theground x seconds after launch is modeled by the quadratic function: y =-16x2 + 132x + 6.How many seconds did it take the rocket to reach its maximum height?

A Bottle Rocket Is Launched Straight Up Its Height In Feet Y Above Theground X Seconds After Launch Is Modeled By The Quadratic Function Y 16x2 132x 6How Many S class=

Sagot :

Answer:

(C)4.125 seconds

Explanation:

The quadratic function modeling the rocket's movement is:

[tex]y=-16x^2+132x+6[/tex]

To determine the number of seconds it takes the rocket to reach its maximum height, we are being asked to find the equation of the line of symmetry.

For a quadratic function of the form y=ax²+bx+c, the equation of the line of symmetry is:

[tex]x=-\frac{b}{2a}[/tex]

In the given equation:

a = -16, b = 132

Therefore:

[tex]\begin{gathered} x=-\frac{132}{-2\times16} \\ x=4.125 \end{gathered}[/tex]

It takes the rocket 4.125 seconds to reach its maximum height.

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