Applications of Quadratic Functions

A square is altered so that one dimension is increased by 5 meters and the other dimension is increased by 3. If the area of the resulting rectangle is 99 m², find the area of the original square?

• 6 m

• 36 m²

• 14 m²

• 169 m²

If the area of the given rectangle is 39 ft², find the value of x.

• 5 ft

• 11 ft

• 25 ft

• 10 ft

Given two consecutive positive integers such that the sum of their squares is 145, which equation could be used to solve this equation?

• $x\ +\ \left(x+1\right)\ =\ 145$ 

• $x^2+\left(x+1\right)^2=145$

• $x^2+\left(x+1\right)\ =\ 145$

• $\left(x\ +\ \left(x+1\right)\right)^{2\ }=145$

A square was altered so that one side is increased by 9 inches and the other side is decreased by 2 inches. The area of the resulting rectangle is 60 in². What is the length of the sides of the square?

• 13 in.

• 36 in.

• 6 in.

• 12 in

April shoots an arrow upward at a speed of 80 ft/sec from a platform of 25 ft. high. The pathway of the arrow can be represented by the equation h = -16t² + 80t + 25, where h is the height and t is the time in seconds. What is the maximum height that the arrow reaches?

• 80 ft.

• 90 ft.

• 140 ft.

• 125 ft.

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.4

CCSS.HSA.SSE.A.1

A rock is dropped from a bridge 320 ft. above a river. The pathway that the rock takes can be modeled by the equation h = -16t² + 320. How long will it take for the rock to reach the river (i.e. hit the "ground")?

• 2.5 sec

• 3.5 sec

• 4.5 sec

• 3.8 sec

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.4

CCSS.HSA.SSE.A.1

A toy rocket is launched and its height is modeled by the equation h = -16t² + 32t + 48. What is the initial heigh of the object?

• 48 ft.

• 16 ft.

• 32 ft.

• 2 ft.

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.4

CCSS.HSA.SSE.A.1

Given three consecutive positive integers, such that the product of the first and third integer is 29 more than the second integer. Which equation could be used to solve this problem?

• (x + 1) - 29 = x(x + 2)

• x + 1 = x(x + 2) + 29

• (x + 1) + x(x + 2) = 29

• x(x+2) = (x + 1) + 29

Tags

CCSS.HSA.CED.A.1

The ages of three students are in consecutive order. The product of the ages of the two older students is 30. State the age of each student.