**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)*

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 isx = 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 , 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 . 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*.

(3 Marks)

(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) = -x ^{2} + 4x -3* can be expressed in the form of

*f(x) = -( x – 2)*, where

^{2 }+ k*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

*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)

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