The equation, y=−16x2+32x+24 , represents the height, in feet, of a firework x seconds after it is launched. What is the maximum height of the firework? Enter your answer in the box. feet

Answer :

Answer:

40

Step-by-step explanation:

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The maximum height of the firework is 40 feet.

What is maximum height?

'The maximum height of the object is the highest vertical position along its trajectory.'

According to the given problem,

y = -16x²+32x+24

For maximum height,

The slope of y with respect to x has to be 0.

⇒ [tex]\frac{dy}{dx}[/tex] = 0

Now, [tex]\frac{d(-16x^{2} +32x+24)}{dx}[/tex] = -32x +32

⇒-32x + 32 = 0

⇒ 32 = 32x

⇒1 = x or x = 1 second

Therefore after 1 second, the firework reaches maximum height.

Now, we put the value of x = 1 second in the equation: y = -16x²+32x+24

⇒ -16(1)² + 32(1) +24

= -16+32+24

= 40 feet

Hence, we can conclude that after 1 second, the firework reaches a maximum height of 40 feet.

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