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mathematics UK Year 12 Mathematics (AS)
 
Solved problems for the chapter:
 

Different quadratic functions

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Irrational equation
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Quadratic equation
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Vieta's formula
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Quadratic function
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Detailed solution steps are available at:
 
https://en.openprof.com/wb/chapter:different_quadratic_functions/5462/


Example 1.

Show that the equations and are equivalent.

    
Example 2.
Solve the equation:

    
3.
Solve the equation:

    
4.
Solve the irrational equation:

    
5.
Solve the irrational equation:

    
6.
Solve the irrational equation:

    
7.
Solve the irrational equation:

    
8.
Solve the equation:

    

9.
Solve the equation:

    
10.

If , solve the equation below:


    
11.

If , solve the equation:


    
12.

In the equation, eliminate the absolute value and solve it:


    
13.

In the equation, eliminate the absolute value and solve it:


    
14.

Write down the remaining two forms of the quadratic function:


    
15.

Find an expression for the quadratic function f(x) with intercept of 1 on the y-axis, whose curve passes through the point (- 2, 3) and intersect the bisector of the odd quadrants at .

    
16.

Write down the remaining two forms of the quadratic function:


    
17.

Write down the remaining two forms of the quadratic function:


    
18.

Write down the remaining two forms of the quadratic function:


    

19.

Write down the remaining two forms of the quadratic function:


    
20.

Write down the remaining two forms of the quadratic function:


    
21.

For a family of quadratic functions ; find and write that function for which the sum of roots is .

    
22.

The function is given. Write down the zeros of the function and the coordinates of the intersection of the graph with the ordinate axis.

    
23.
Find unknowns a, b and c to which the following applies:

    
24.

What are the possible values of for which the solution of the equation will be rational numbers:


    
25.

Obtain for what values of a and b will the solution of the equation below be rational numbers:


    
26.

The equation is given.


  • Consider the equation with respect to the value of the parameter , show that the solution will be rational numbers for .

  • For which rational number will the solution of the equation ?

    
27.

The equation is given:


  • Solve the equation for .


  • For which rational number will the solution of the equation be equal to .

    
28.

Consider the equation below with respect to the value of the parameter , show that the solution will be rational numbers:


    

29.

Consider the equation below with respect to the value of the parameter , show that the solution will be rational numbers:


    
30.

Sets A and B are sets of rational numbers:






  • Write down their elements.

  • Write down the elements of the set A-B.

    
31.

The equation is given.


  • Solve the equation above for


  • For which rational number will the solution of the equation be equal to .