Unit 5
7 marks · NormalThe graph below shows the curve .
State the points where the curve cuts the x-axis.
Use the graph or otherwise to write down the equation solved at the y-intercept. Find the y-intercept.
Describe the transformation that maps the graph of to the graph of .
Solve the inequality . Give the solution set for .
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
Show answer
(a) (-2, 0) and (2, 0) · must show Both x-intercepts
(b) Equation: y = x² - 4 when x = 0; y-intercept is (0, -4). · must show Substitute x=0 to find y
(c) Translation 2 units to the right. · must show Translation right
(d) -2 < x < 2 · must show Correct solution set for the inequality
Show mark scheme and worked solution
Marking points
B1 (a) · 1 mark · Both correct x-intercepts identified; values must be exact.
M1 (b) · 1 mark · Substitutes x=0 to form correct equation.
A1 (b) · 1 mark · Gives correct y-intercept.
B2 (c) · 2 marks · Correctly states it is a translation right by 2 units.
M2 (d) · 1 mark · Sets up and solves x^2 - 4 < 0 (i.e. finds values for x^2 < 4).
A2 (d) · 1 mark · Gives final solution -2 < x < 2.
Worked solution
a) The curve crosses the x-axis where y=0: x^2-4=0 ⇒ x^2=4 ⇒ x=±2. Points: (-2, 0) and (2, 0).
b) At x=0: y=0^2-4=-4, so y-intercept is (0, -4).
c) y = (x-2)^2 - 4 is a translation of y = x^2 - 4 by 2 units to the right.
d) x^2-4 < 0 ⇒ x^2 < 4 ⇒ -2 < x < 2.