Quadratic functions can also be written in the form y = (x-p) (x-q) In this task
ID: 3114731 • Letter: Q
Question
Quadratic functions can also be written in the form y = (x-p) (x-q) In this task, you will investigate the effect p and q have on the shape of the graph of a quadratic function. Using https://www.desmos.com/ alculator, plot at least 6 functions for y = (x-p)(x-q) where p and q are values between -3 and 3. They may be the same or different values 5. Use an appropriate scale and include screenshots in your submission. [2 marks] 6. Using appropriate mathematical language and terms, describe fully the significance of p and q on the graph of y = (x-p) (x-q) [2 marks] 7. Write the value for the axis of symmetry in terms of n and q I mark]Explanation / Answer
6) p and q are the points on graph where y is 0 i.e the value of quadratic function at x=p and x=q is zero.
7) given quadratice function = (x-p)(x-q) =
x^2 - xq -px +pq = x^2 -x(q+p) +pq
Therefore the x axis of symmetry is (q+p)/2
8) value of a=-1/2
Value of b= +2
X cordinate of c = (a+b)/2= (-0.5+2)/2 = 1.5/2 = 0.75