# QUIZ 2A: Quadratic Functions and Equations

Intermediate Algebra 1033C Page (1)

QUIZ 2A: Quadratic Functions and Equations

Student Name: Last, First Valencia ID:

1) Solve: ๐๐ โ ๐ = ๐๐

SOLUTION:

2) Solve: ๐๐๐ โ ๐๐๐ = ๐

SOLUTION:

3) Solve: ๐๐๐ + ๐ โ ๐๐๐ = ๐

SOLUTION:

4) Solve: ๐๐๐ โ ๐๐ = ๐

SOLUTION:

5) Solve: โ๐๐๐ + ๐๐๐๐ = ๐๐๐

SOLUTION:

6) Solve: ๐๐๐ + ๐๐ = ๐๐๐

SOLUTION:

7) Solve: (๐ โ ๐๐)๐ โ ๐๐ = ๐๐

SOLUTION:

Intermediate Algebra 1033C Page (2)

8) Solve: (๐๐ โ ๐)๐ + ๐๐ = ๐๐

SOLUTION:

9) Solve: 2๐๐ โ ๐๐ = ๐

SOLUTION:

10) Solve: 3๐๐ + ๐๐ + ๐ = ๐

SOLUTION:

11) Solve: ๐ โ ๐

๐ =

๐

๐๐

SOLUTION:

12) Solve: ๐ + ๐๐

๐ = ๐

SOLUTION:

13) Solve: ๐(๐๐ โ ๐)๐ โ ๐(๐๐ โ ๐) = ๐ SOLUTION:

14) Solve: ๐๐

๐+๐ +

๐

๐โ๐ =

๐โ๐๐

๐๐+๐โ๐

SOLUTION:

Intermediate Algebra 1033C Page (3)

15) Solve: ๐๐

๐โ๐ +

๐

๐ = ๐

SOLUTION:

16) Find the missing term/terms

i) โฆ + โฏ + ๐๐ = (๐๐ + โฏ )๐ ii) ๐๐๐๐ โ โฏ + ๐ = (โฆ โฆ โฆ )๐

iii) โฆ โ ๐๐ + ๐ = (โฆ โฆ โฆ )๐ iv) โฆ โ ๐๐๐ + โฏ = (๐๐ โฆ โฆ )๐

v) โฆ โ ๐๐๐ + โฏ = (โฆ โฆ ๐๐)๐ vi) โฆ + โฏ + ๐ = (๐๐ + โฏ )๐

vii) โฆ + ๐๐๐๐ + โฏ = (๐๐ + โฏ )๐ viii) โฆ โ ๐๐๐ + ๐๐ = (โฆ โฆ โฆ )๐

17) Solve: ๐ = ๐โ๐ SOLUTION:

18) Solve: โ๐ โ ๐ = ๐ โ ๐

SOLUTION:

19) Solve: โ๐๐ โ ๐ + ๐ = ๐

SOLUTION:

20) Solve: โ๐๐ โ ๐๐ = ๐

SOLUTION:

21) Solve: |๐๐ + ๐| = ๐๐

SOLUTION:

Intermediate Algebra 1033C Page (4)

22) Find two consecutive whole numbers such that the sum of their squares is ๐๐๐. SOLUTION:

23) Find the number ๐ for which ๐ = ๐ is a solution of the equation ๐ + ๐๐ = ๐ โ ๐ + ๐๐๐ SOLUTION:

24) The equation ๐๐๐ + ๐๐ + ๐ = ๐ has repeated root. Find the value of ๐. SOLUTION:

25) Find ๐ such that the equation โ๐ + ๐๐ โ ๐๐๐ = ๐ has repeated root. SOLUTION:

26) Find ๐ such that the equation ๐๐๐ + ๐ + ๐ = ๐ has a repeated real solution. SOLUTION:

27) The function ๐ is defined by (๐) = ๐๐ โ ๐๐ + ๐ . Find the two values of ๐ for which ๐(๐) = ๐(๐) SOLUTION:

28) The function ๐ is defined by (๐) = ๐๐๐ + ๐๐ + ๐ . Given that ๐(๐) = ๐, ๐(โ๐) = ๐๐ and ๐(๐) = ๐, find the values of ๐, ๐ ๐๐๐ ๐. SOLUTION:

Intermediate Algebra 1033C Page (4)

29) If a toy rocket is launched vertically upward from ground level with an initial velocity of

๐๐๐ ๐๐๐๐ ๐๐๐ ๐๐๐๐๐๐ , then its height ๐ after ๐ seconds is given by the equation

๐(๐) = โ๐๐๐๐ + ๐๐๐๐ (if air resistance is neglected).

i) How long will it take for the rocket to return to the ground?

ii) After how many seconds will the rocket be 112 feet above the ground?

iii) How long will it take the rocket to hit its maximum height?

iv) What is the maximum height?

SOLUTION:

30) Joseph jumped off of a cliff into the ocean in Miami while vacationing with some friends. His

height as a function of time is given by ๐(๐) = โ๐๐๐๐ + ๐๐๐ + ๐๐๐ , where ๐ is the time in seconds

and ๐ is the height in feet.

i) How long did it take for Joseph to reach his maximum height? ii) What was the highest point that Joseph reached? iii) Joseph hit the water after how many seconds? SOLUTION:

31) A falcon dives toward a pigeon on the ground. Its height as a function of time is given by (๐) = โ๐๐๐๐ โ ๐๐๐๐ + ๐๐๐ , where ๐ is the height, ๐ is the time. Estimate the time the pigeon has to escape. SOLUTION:

Intermediate Algebra 1033C Page (5)

32) A golf ball is hit from the top of a tower. Its height defined by the function

, ๐(๐) = โ๐๐๐ + ๐๐๐ + ๐๐, where ๐ represents the time in seconds since the ball was hit, and ๐

represents the height of the ball above the ground in metres.

i) What is the height of the tower?

ii) How long will it take the ball to hit its maximum height?

iii) Find the maximum height reached by the ball?

iv) After how many seconds the ball will hits the ground?

SOLUTION:

33) A baseball is thrown from an initial height of ๐ ๐ and reaches a maximum height of ๐ ๐,

๐ ๐๐๐๐๐๐ ๐ after it is thrown.

i) Write a quadratic equation which models this situation.

ii) At what time does the ball hit the ground?

SOLUTION:

HINT: Quadratic Vertex Form

๐ = ๐(๐ โ ๐ฏ)๐ + ๐ฎ

34) The area of a rectangular window is to be ๐๐๐ square centimeters. If the length exceeds the

width by 2 centimeter, what are the dimensions?

SOLUTION:

Intermediate Algebra 1033C Page (6)

35) The sum of the consecutive integers ๐, ๐, ๐, . . , ๐ is given by the formula ๐

๐ ๐(๐ + ๐) How many

consecutive integers, starting with๐, must be added to get a sum of ๐๐๐? SOLUTION:

36) If a polygon of n sides has ๐

๐ ๐(๐ โ ๐) diagonals, how many sides will a polygon with 65

diagonals have? Is there a polygon with 80 diagonals? SOLUTION:

37) Let ๐(๐) = ๐๐ โ ๐ + ๐ ๐๐ง๐ ๐(๐) = ๐๐ โ ๐. Find (๐ โ ๐)(๐), ๐๐ง๐ (๐ + ๐)(โ๐) SOLUTION:

38) Let ๐(๐) = ๐๐ โ ๐ + ๐ ๐๐ง๐ ๐(๐) = ๐๐ โ ๐. Find (๐ โ ๐)(๐), ๐(๐(๐)) ๐๐ง๐ ๐(๐(โ๐))

SOLUTION:

39) Determine the quadratic function whose graph is given

Intermediate Algebra 1033C Page (7)

40) Graph the quadratic function 41) Graph the quadratic function

๐ = ๐๐ โ ๐๐ โ ๐ ๐ฆ = โ(๐ + ๐)๐ + ๐

and identify all the key features and identify all the key features

SOLUTION: SOLUTION:

i) Axis of Symmetry: i) Axis of Symmetry:

ii) Vertex : ii) Vertex :

iii) Circle one: Minimum or Maximum iii) Circle one: Minimum or Maximum

iv) Circle one: Opens up or Opens Down iv) Circle one: Opens up or Opens Down

v) ๐ โ ๐๐๐๐๐๐๐๐๐: v) ๐ โ ๐๐๐๐๐๐๐๐๐:

vi) ๐ฟ โ ๐๐๐๐๐๐๐๐๐(๐): vi) ๐ฟ โ ๐๐๐๐๐๐๐๐๐(๐):

vii) Domain: vii) Domain:

viii) Range: viii) Range:

ix) ๐ is Increase on the interval: ix) ๐ is Increase on the interval:

x) ๐ is Decrease on the interval: x) ๐ is Decrease on the interval:

xi) Standard form: xi) Standard form:

xii) Vertex form: xii) Vertex form:

xiii) Intercept form/ Factored Form: xiii) Intercept form/ Factored

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