Everything Maths Grade 11

CHAPTER 11. QUADRATIC FUNCTIONS ANDGRAPHS 11.2

The x-intercept is obtained bysetting y = 0. This gives:

0 =−

1

2

(xint+ 1)^2 − 3

3 =−

1

2

(xint+ 1)^2

− 3 .2 = (xint+ 1)^2

−6 = (xint+ 1)^2

which has no real solutions. Therefore, there areno x-intercepts.

We also know that the axis of symmetry is parallel to the y-axis and passes throughthe turning point.

− 1

− 2

− 3

− 4

− 5

− 6

− 7

4 3 − 2 − − 1 − 1 2 3 4

�

�(0;− 3. 5 )

(−1;− 3 )

Figure 11.2: Graph of the function f(x) =−^12 (x + 1)^2 − 3

See video: VMfkk at http://www.everythingmaths.co.za

Exercise 11 - 5

1. Draw the graph of y = 3(x− 2)^2 + 1 showing all the intercepts with the axes as well as the
   coordinates of the turning point.


2. Draw a neat sketch graph of the function defined by y = ax^2 + bx+ c if a > 0 ; b < 0 ; b^2 = 4ac.

More practice video solutions or help at http://www.everythingmaths.co.za

(1.) 011h (2.) 011i