SPM Questions for Quadratic Functions
- The Basic of quadratic functions (SPM 2010)
- Determine max and min values of quadratic function (SPM2009)
- How to sketch the graph of quadratic functions (SPM2010)
- How to find the range of values of x in Quadratic inequalities (2007, 2006)
The Basic of quadratic functions – SPM 2010 Paper 1 Question 4
Diagram 4 shows the graph of a quadratic function y = f(x)
(a) The roots of the equation f(x) = 0
(b) The equation of the axis of symmetry of the curve
a) The roots of equation f(x)=0 are -1 and 3.
(Tips: From the graph we know that when y=0, so the value of x are -1 and 3)
b) The axis of symmetry is x = 1.
Determine max and min values of quadratic function –SPM 2009 Paper 1 Question 5
5. Diagram 5 shows the graph of a quadratic function , where p and q are constants.
(a) the value of p.
(b) the equation of the axis of symmetry
(Tip: You have to understand the info given in . The negative sign here tell us it has a maximum point (-3, 0), so x = – 3, q = 0. )
a) From the maximum point, we know x = – 3
substitute x = – 3 into ( x+p ),
– 3 + p = 0
p = 3
b) The equation of the axis of symmetry is x = – 3
SPM 2009 Paper 1 Question 6
6. The quadratic function , where a is a constant, has maximum value 8. Find the values of a.
(Tips: Remember, convert f(x) into the form of by using completing the square to find out the “a” value)
How to sketch the graph of quadratic functions – SPM 2010 Paper 1 Question 6
6. The quadratic function f(x) = -x2 + 4x -3 can be expressed in the form of
f(x) = -( x – 2)2 + k , where k is constant.
(a) find the value of k.
(b) sketch the graph of the function f(x) on the given axes.
(Tips: Max point meant graph open downward, using 3 points, (2,1), (1,0), (3,0) to draw the graph)
How to find the range of values of x in Quadratic inequalities -SPM 2007 paper 1 Question 5
Find the range of values of x for which . (3 marks)
SPM 2006 paper 1 Question 5
Find the range of values of x for . (2 marks)