QF Test

Name: ___________________________ 		

Multiple Choice
Identify the choice that best completes the statement or answers the question.

____	1.	Identify the y-intercept of the graph of this quadratic function: 
A.	37	B.	0	C.	39	D.	4	

____	2.	A rectangular dog pen is to be enclosed with 20 m of fencing. The area of the dog pen, A square metres, is modelled by the function , where x is the width, in metres. What is the width that gives maximum area? Write the answer to the nearest tenth, if necessary.
A.	5 m	C.	20 m	
B.	25 m	D.	10 m	

____	3.	Which of the following describes the translation that would be applied to the graph of  to get the graph of ?
A.	Translate 7 units right	C.	Translate 7 units down	
B.	Translate 7 units up	D.	Translate 7 units left	

____	4.	Match the quadratic function  to a graph below.
A.		C.		
B.		D.		

____	5.	Determine an equation of this graph of a quadratic function.

A.		C.		
B.		D.		

____	6.	Which equation represents the same quadratic function as ?
A.		C.		
B.		D.		

____	7.	Write this equation in standard form: 
A.		C.		
B.		D.		

____	8.	A quadratic function has zeros –3 and 8. What is the equation of the axis of symmetry of its graph?
A.		B.		C.		D.		

____	9.	Write  in general form.
A.		C.		
B.		D.		

____	10.	Determine the zeros of this quadratic function: 
A.	-4 and 8	B.	4 and -8	C.	4 and 8	D.	-4 and -8	

____	11.	For this graph of a quadratic function, write the equation in factored form.

A.		C.		
B.		D.		

Short Answer

	1.	Write  in standard form, then identify the coordinates of the vertex.

	2.	The graph of a quadratic function passes through A(3, 12) and has x-intercepts 1 and 5. Write an equation of the graph in factored form.

	3.	A rectangular lot is bordered on one side by a building and the other 3 sides by 300 m of fencing. Determine the area of the largest lot possible.

	1.	For the quadratic function 
a)	Identify:
	i)	the direction of opening
	ii)	the vertex
	iii)	the equation of the axis of symmetry
	iv)	the intercepts
	v)	the domain and range of the function
b)	Sketch a graph. Explain your strategy.

QF Test
Answer Section

MULTIPLE CHOICE

	1.	ANS:	C	PTS:	0	DIF:	Easy	
REF:	4.1 Properties of a Quadratic Function		LOC:	11.RF4
TOP:	Relations and Functions	KEY:	Procedural Knowledge

	2.	ANS:	A	PTS:	0	DIF:	Moderate	
REF:	4.1 Properties of a Quadratic Function		LOC:	11.RF4
TOP:	Relations and Functions	KEY:	Problem-Solving Skills | Procedural Knowledge

	3.	ANS:	A	PTS:	0	DIF:	Easy	
REF:	4.3 Transforming the Graph of y = x^2		LOC:	11.RF3
TOP:	Relations and Functions	KEY:	Conceptual Understanding

	4.	ANS:	A	PTS:	0	DIF:	Easy	
REF:	4.4 Analyzing Quadratic Functions of the Form y = a(x - p)^2 + q	
LOC:	11.RF3	TOP:	Relations and Functions	KEY:	Conceptual Understanding

	5.	ANS:	D	PTS:	0	DIF:	Moderate	
REF:	4.4 Analyzing Quadratic Functions of the Form y = a(x - p)^2 + q	
LOC:	11.RF3	TOP:	Relations and Functions	KEY:	Procedural Knowledge

	6.	ANS:	D	PTS:	0	DIF:	Easy	
REF:	4.5 Equivalent Forms of the Equation of a Quadratic Function	
LOC:	11.RF4	TOP:	Relations and Functions	KEY:	Procedural Knowledge

	7.	ANS:	C	PTS:	0	DIF:	Moderate	
REF:	4.5 Equivalent Forms of the Equation of a Quadratic Function	
LOC:	11.RF4	TOP:	Relations and Functions	KEY:	Procedural Knowledge

	8.	ANS:	A	PTS:	0	DIF:	Easy	
REF:	4.6 Analyzing Quadratic Functions of the Form y = ax^2 + bx + c	
LOC:	11.RF4	TOP:	Relations and Functions	KEY:	Procedural Knowledge

	9.	ANS:	C	PTS:	0	DIF:	Easy	
REF:	4.6 Analyzing Quadratic Functions of the Form y = ax^2 + bx + c	
LOC:	11.RF4	TOP:	Relations and Functions	KEY:	Procedural Knowledge

	10.	ANS:	A	PTS:	0	DIF:	Easy	
REF:	4.6 Analyzing Quadratic Functions of the Form y = ax^2 + bx + c	
LOC:	11.RF4	TOP:	Relations and Functions	KEY:	Procedural Knowledge

	11.	ANS:	A	PTS:	0	DIF:	Moderate	
REF:	4.6 Analyzing Quadratic Functions of the Form y = ax^2 + bx + c	
LOC:	11.RF4	TOP:	Relations and Functions	KEY:	Procedural Knowledge

SHORT ANSWER

	1.	ANS:	
; (, )

PTS:	0	DIF:	Moderate	
REF:	4.5 Equivalent Forms of the Equation of a Quadratic Function	
LOC:	11.RF4	TOP:	Relations and Functions	
KEY:	Conceptual Understanding | Procedural Knowledge

	2.	ANS:	

PTS:	0	DIF:	Moderate	
REF:	4.6 Analyzing Quadratic Functions of the Form y = ax^2 + bx + c	
LOC:	11.RF4	TOP:	Relations and Functions	KEY:	Procedural Knowledge

	3.	ANS:	
11 250 m2

PTS:	0	DIF:	Moderate	
REF:	4.7 Modelling and Solving Problems with Quadratic Functions	
LOC:	11.RF4	TOP:	Relations and Functions	
KEY:	Problem-Solving Skills | Procedural Knowledge

PROBLEM

	1.	ANS:	
Compare  with . 
a)	i)	a is negative, so the graph opens down.
	ii)	p = 4 and q = –8, so the coordinates of the vertex are: (4, –8)
	iii)	In general, the equation of the axis of symmetry is ; so for this graph it is .
	iv)	For the y-intercept, substitute  in .
		
		The y-intercept is –40.

		For the x-intercept, substitute  in .
		
		This equation has no solution because a square number cannot be negative. 
		So, there are no x-intercepts.
	v)	The domain is: 
		The graph opens down, so the vertex is a minimum point with y-coordinate –8. The 			range is: , 

b)	The graph of  is congruent to the graph of .
	On a grid, mark a point at the vertex (4, –8). Use the step pattern. Multiply each vertical step by -2 because the graph is a vertical expansion of factor 2 of the graph of .

PTS:	0	DIF:	Moderate	
REF:	4.4 Analyzing Quadratic Functions of the Form y = a(x - p)^2 + q	
LOC:	11.RF3	TOP:	Relations and Functions	
KEY:	Communication | Conceptual Understanding | Procedural Knowledge