Graphs 5

4 marks · Hard

The equation of a quadratic curve is . The graph of is transformed to the graph of .

Write down the equation of the transformed graph in terms of .

Calculate the coordinates of the new vertex (minimum point) after these transformations.

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.

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Common mistakes: Translation and scaling order wrong; not recalculating minimum correctly

Show mark scheme and worked solution

Marking points

M1 · 1 mark · Multiplies original function by 3 and translates x and y correctly.

A1 · 1 mark · Correctly writes the equation as or equivalent simplified form.

M2 · 1 mark · Finds the vertex/minimum point for the original graph and correctly applies the transformations (translation, stretch, and vertical translation) in the right order.

A2 · 1 mark · Gives the exact coordinates of the minimum point after transformation, fully simplified.

Worked solution

First, the original vertex of occurs at :

So, the vertex is at (2, -3).

Apply the x-translation of +2: replace by , so the function is .

Then, multiply entire function by 3 and subtract 4:

Expand

Vertex of is at

So the vertex is at (4, -13).