Tasks | Early Adolescence | Trinomials

Tasks - Years 10, 11 & 12

Trinomials: X Intercepts of their Graphs   by Thelma Perso, Senior Curriculum Officer Mathematics

Phase of Development:   Early Adolescence - Late Adolescence

Learning Area/s:	Mathematics
Strand/s	Substrand/s
Algebra	Understand Graphs Represent Variation Understand Symbols
Working Mathematically	Apply and Verify
Expected Outcomes:	Students understand the relationship between the zeros of a quadratic equation and their graphical application/interpretation
Context:	Year 9,10, Foundations of Mathematics. I have used this investigations successfully with year 9,10 and 11 students.
Learning Activities/ Experience:	Assumed Knowledge Students know how to factorise trinomials. This activity gives legs to the value of the skill of factorising trinomials - the visual approach generates understanding.
Resources:	Graphics Calculators Worksheet

Worksheet

Trinomials : X-Intercepts of Their Graphs

1. Use your calculator to graph y = x² + 6x + I

2. Now clear that from the screen and graph y = ( x + 2 )(x + 4). What do you notice?

   

   Why does this happen?

   

3. Use your TRACE and ZOOM buttons to find the x intercepts for y = x² + 6x + 8 ; put the results in the table below and then complete the table for the other functions.

   Function	Expanded Form	Sketch	x intercepts
   y = (x + 2)(x + 4)	y = x2 + 6x + 8		- 2, - 4
   	y = x2 + 6x + 5
   	y = x2 + 9x - 14
   	y = x2 + 7x - 21
   	y = x2 - 6x - 55

   Do you notice a relationship between the x intercepts and the x coefficient?

   

   Do you notice a relationship between the x intercepts and the constant? Write about it.

   

   

    

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