Unit 9

7 marks · Easy

A function is defined by . The graph of is shown below.

Graph of \( y = x^2 \ )

(a)

Write down the equation of the curve obtained when the graph of is reflected in the y-axis.

[2 marks]

(b)

The point on has coordinates (2, 4). The point is the image of under a stretch, scale factor 3, parallel to the y-axis.

Work out the coordinates of point after this transformation.

[2 marks]

(c)

A cuboid has length 5 cm, width 2 cm, and height 4 cm. One diagonal passes from one vertex (corner) to the opposite vertex through the interior of the cuboid.

Using Pythagoras' theorem in 3D, calculate the length of this diagonal.

[3 marks]

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) y = f(-x) or y = (-x)^2 = x^2 · must show y = f(-x) or y = x^2

(b) (2, 12) · must show x=2, y=12

Common mistakes: writing y = -f(x) instead of y = f(-x) in part (a); stretching x not y in part (b); incorrect formula for diagonal in part (c)

Show mark scheme and worked solution

Marking points

B1 (a) · 1 mark · Correctly writes the equation for a reflection in the y-axis.

B2 (a) · 1 mark · Gives the result in correct algebraic form (e.g. y = x^2 for this function, acknowledging the symmetry).

M1 (b) · 1 mark · States or uses correct method for stretching parallel to y-axis (scaling y by 3, x unchanged).

A1 (b) · 1 mark · Gives the correct coordinates after transformation: (2,12). (follow-through)

M1 (c) · 1 mark · Uses correct 3D Pythagoras approach: diagonal = sqrt(l^2 + w^2 + h^2).

A1 (c) · 2 marks · Gives correct calculation \( \sqrt{25+4+16}\ ) and final value, with 3 sf: 6.71 cm. (follow-through)

Worked solution

(a) Reflection in the y-axis means replace x by -x:

So equation is y = x^2.

(b) Stretch with scale factor 3 parallel to y-axis:

Multiply only the y-coordinate by 3; x stays the same.