Question 1:
Show that the equation of the straight line passing through the points (0, p) and (p, 0) is 𝑦 + 𝑥 = 𝑝 y+x=p.
Question 2:
Given the function 𝑓 ( 𝑥 ) = − 2 𝑥 2 + 4 𝑥 − 6 f(x)=−2x 2 +4x−6:
(a) Identify the function and explain why.
(b) Find the vertex of the function.
(c) Find the intercepts of the function with the axes.
(d) Sketch the graph of the function on a Cartesian plane.
Question 3:
Consider the function 𝑓 ( 𝑥 ) = 2 ( 𝑥 − 3 ) ( 𝑥 + 1 ) f(x)=2(x−3)(x+1):
(a) Is the curve open upwards or downwards? Explain.
(b) Find the vertex and intercepts of the curve.
(c) What is the axis of symmetry of the curve?
(d) Sketch the curve on a Cartesian plane.
Question 4:
Sketch the graph of 𝑦 = − ( 𝑥 + 4 ) ( 𝑥 − 9 ) y=−(x+4)(x−9).
Question 5:
Find the equation of the line that is parallel to the line 4 𝑦 + 5 𝑥 = 6 4y+5x=6 and passes through the point ( 8 , 5 ) (8,5).
Question 6:
(a) Show that the point ( − 1 , − 4 ) (−1,−4) lies on the line 𝑦 = 3 𝑥 − 1 y=3x−1. (b) Find the equation of the line that is parallel to the line 𝑥 + 2 𝑦 + 8 = 0 x+2y+8=0 and passes through the point ( − 2 , − 3 ) (−2,−3).
Question 7:
(a) Given that the line 𝑦 = 3 𝑥 + 𝑎 y=3x+a passes through ( 1 , 4 ) (1,4), find the value of 𝑎 a.
(b) Sketch the graph of 𝑦 = − 2 𝑥 2 − 6 𝑥 − 9 y=−2x 2 −6x−9.