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Quadratic Equations

Quadratic equations describe the motion of a baseball after it connects with a bat, and the acceleration of gravity at the Earth's orbit.

Word Problems

         

In 36 years, Frank will be half the square of the age he was 4 years ago. How old is Frank now?

A firework is shot from the top of a hill that is 60 feet above a lake. The firework's height above the surface of the lake \(t\) seconds after launch is given by

\[ h = - 16t^2 + 160 t + 60 \]

Given that the firework explodes at the highest point of it's path, at what height above the surface of the lake will it explode?

In the above image, the blue picture is 3 inches longer than it is wide. On all sides, the yellow frame is 5 inches around. If the area of the picture is 378, what is the area of the frame?

Two taps \(A\) and \(B\) can fill a swimming pool in 3 hours. If turned on alone, it takes tap A 4 hours less than tap B to fill the same pool. How many hours does it take tap A to fill the pool? (Round your answer to three decimals places.)

Mark has a rectangular plot of land with area \( 357 \) square feet and perimeter \( 76\) feet. What is the length (longer dimension) of Mark's land?

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