The diagram below shows the graphs of 𝑓(𝑥) = -𝑥2 -𝑥 + 6 and 𝑔 (𝑥) = 𝑚𝑥 + 𝑐. A (-2 ; 4) is the point of intersections of the graphs.
6.1 Determine the 𝑥-interceptions 𝑓. (4)
6.2 Write down the equation of the axis of symmetry of 𝑓. (2)
6.3 Determine the range of 𝑓. (3)
6.4 Write down the equation of 𝑔 in the form of 𝑔(𝑥) = 𝑚𝑥 + 𝑐. (3)
6.5 Write down the average gradient between points A and D. (1)
6.6 Determine the equation of ℎ, if ℎ is the reflection of 𝑓 about the 𝑥-axis and then translated 3 units to the right . Leave your answer in the form ℎ(𝑥) = 𝑎(𝑥 + 𝑝)2 + 𝑞. (3)
6.7 Write down the values of 𝑥 for which 𝑓(𝑥) > 0. (2)
6.8 If 𝑓(𝑝) = 𝑓(𝑟) = 4, calculate the value of 𝑝 – 𝑟 if 𝑟 < 0 (4)
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