Quadratic Word Problems

Sketch a graph• The path of a baseball is given by the function

where f(x) is the height of the baseball in feet and x is the distance from home plate in feet. Enter the function into a graphing calculator and draw a sketch.

2( ) 0.0032 3f x x x

Answer• Put function into y=, adjust window and graph.

Max/Min/Vertex• What is the maximum height reached by the baseball?

Answer• 2nd TRACE 4:maximum• use left/right arrows to move cursor to the left of the hump

and press enter• use right arrow to move cursor to the right of the hump and

press enter• Press enter

Maximum height = 81.125 feet

Zero/Root/X-int• What is the horizontal distance from home plate when the

ball hits the ground?

Answer• 2nd TRACE 2:zero• use left/right arrows to move cursor to the left of the x-int and

press enter• use right arrow to move cursor to the right of the x-int and

press enter• Press enter

• Horizontal distance = 315.47174 feet

Pizza!!• The quadratic function

gives the price of pizza in dollars as a function of the diameter x. Does the model give a reasonable price for a 30 inch pizza?

2( ) 0.00625 0.2625 2P x x x

Answer• Put function into y=, adjust window and graph.• 2nd TRACE 1:value• 30 press enter

• $15.50 for a 30 in pizza seems too low

Pizza Snacks• Assume the pizza maker is willing to make 4 inch pizza snacks.

Does the model give a price that is reasonable to pay?

Answer• Put function into y=, adjust window and graph.• 2nd TRACE 1:value• 4 press enter

• $3.15 for a 4 in pizza seems too high