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Question
Let \(f(x) = 2{x^2} + 4x – 6\) .
Express \(f(x)\) in the form \(f(x) = 2{(x – h)^2} + k\) .
Write down the equation of the axis of symmetry of the graph of f .
Express \(f(x)\) in the form \(f(x) = 2(x – p)(x – q)\) .
Answer/Explanation
Markscheme
evidence of obtaining the vertex (M1)
e.g. a graph, \(x = – \frac{b}{{2a}}\) , completing the square
\(f(x) = 2{(x + 1)^2} – 8\) A2 N3
[3 marks]
\(x = – 1\) (equation must be seen) A1 N1
[1 mark]
\(f(x) = 2(x – 1)(x + 3)\) A1A1 N2
[2 marks]
Question
Let \(f(x) = 3{x^2}\) . The graph of f is translated 1 unit to the right and 2 units down. The graph of g is the image of the graph of f after this translation.
Write down the coordinates of the vertex of the graph of g .
Express g in the form \(g(x) = 3{(x – p)^2} + q\) .
The graph of h is the reflection of the graph of g in the x-axis.
Write down the coordinates of the vertex of the graph of h .
Answer/Explanation
Markscheme
\((1{\text{, }} – 2)\) A1A1 N2
[2 marks]
\(g(x) = 3{(x – 1)^2} – 2\) (accept \(p = 1\) , \(q = – 2\) ) A1A1 N2
[2 marks]
\((1{\text{, }}2)\) A1A1 N2
[2 marks]