Math AA SL: Quadratic Functions

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[Maximum Marks: 5]

Consider the function 
 is the minimum value of the function

a) Show that the two zeros are  and 

b) Find the value of  and 

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[Maximum Marks: 7]

Let . Part of  is shown on the graph below


 
a) Find the x-intercepts of the graph
 
b) i. Write down the equation for the axis of symmetry 
 
ii. Find the y-coordinate of the vertex 

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[Maximum Marks: 6]

Part of the graph for the quadratic function  is below.
The vertex of the function is point R (8,2), and the y-intercept is point S (0,12).

a) Find the equation of the axis of symmetry.

b) The function  can be written in the form: . 
Write down the values of  and .

c) Find the value of  in the function structure above.

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[Maximum Mark: 5]

, where  is the vertex,
and the graph passses 

a) Find the values of  and 

b) Find the value of 

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[Maximum Mark: 6]

Consider . The graph of  has a minimum value when .
The distance between the two zeros of  is 4. 

a) Show that the two zeros are 0 and -4. 

b) Find the value of  and of . 

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[Maximum Marks: 6]

Let 
 
a) Express  in the form 
 
b) Write down the equation of the axis of symmetry of the graph of f.
 
c) Express  in the form 

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[Maximum Marks:7]

Examine 

The graph of f yields a minimum point when n = -2.5

The x-intercepts of p are 9 units away from each other

a) Demonstrate that the two x-intercepts are 2 and -7

b) Solve for the value of r and s

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[Maximum Mark: 6]

Let 

a) Express  in the form .

b) Write down the equation of the axis of symmetry of the graph of .

c) Express  in the form .

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[Maximum Mark: 6]

Let 

a) Express  in the form .

b) Write down the equation of the axis of symmetry of the graph of .

c) Express  in the form .

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[Maximum Mark: 16]

Let , for .

Let  be a quadratic function, such that  and  represents the line of symmetry.

The function  can be represented as 

a) Find 

b) Find both x-intercepts of 

c) Find 

d) Find 

e) Find , such that the tangent of  is the same as the tangent of 

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