SPM Questions for Quadratic Functions

  1. The Basic of quadratic functions (SPM 2010)
  2. Determine max and min values of quadratic function (SPM2009)
  3. How to sketch the graph of quadratic functions (SPM2010)
  4. 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)

State

(a)  The roots of the equation f(x) = 0
(b)  The equation of the axis of symmetry of the curve

(3 marks)

Answer:
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.
x=\frac{-1+3}{2}=1 

(Tips: The axis of symmetry of the curve is the mid-point between -1 and 3) 

Determine max and min values of quadratic function –SPM 2009 Paper 1 Question 5

5. Diagram 5 shows the graph of a quadratic function f(x)=-{{(x+p)}^{2}}+q , where p and q are constants.

State

(a)  the value of p.
(b)  the equation of the axis of symmetry

(2 Marks)

Answer:

(Tip: You have to understand the info given in f(x)=-{{(x+p)}^{2}}+q . 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 f(x)=-{{x}^{2}}+4x+{{a}^{2}} , where a is a constant, has maximum value 8. Find the values of a.
(3 Marks)



(Tips: Remember, convert f(x) into the form of  f(x)=a{{(x+p)}^{2}}+q 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.

(4 marks)





(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 2{{x}^{2}}\le1+x. (3 marks)

SPM 2006 paper 1 Question 5

Find the range of values of x for (2x-1)(x+4)>4+x. (2 marks)

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