Graphs of Functions — Solutions
Full worked solutions, with method and final answer for every part.
Question 1
(a)Set y = 0 and factorise: x² − 2x − 3 = (x−3)(x+1) = 0.
x = 3 or x = −1, so (3, 0) and (−1, 0)
Question 2
(a)Substitute x = 0.
y = −3, so the y-intercept is (0, −3)
Question 3
(a)Set y=0 and factorise: x²−5x+6 = (x−2)(x−3).
x = 2 or x = 3, so (2,0) and (3,0)
Question 4
(a)Substitute x = 0.
y = 6, so (0, 6)
Question 5
(a)x-axis: set y=0, 2x=4, x=2. y-axis: set x=0, y=−4.
(2, 0) and (0, −4)
Question 6
(a)y = x³ is a cubic curve with a point of inflection at the origin — it passes through (0,0) and has rotational symmetry about that point, rising from bottom-left to top-right.
An S-shaped cubic curve through the origin, with point symmetry there
Question 7
(a)Factorise: x²+2x−8 = (x+4)(x−2) = 0.
x = −4 or x = 2
Question 8
(a)Substitute x=0.
y = −8
Question 9
(a)x = −2/(2×1) = −1, then substitute into the equation to find y.
(−1, −9)
Question 10
(a)A quadratic can cross the x-axis 0, 1 (touching), or 2 times.
0, 1, or 2 times
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