Higher November 2018 Paper 3 Q20
20 Curve P has equation \(\quad y = 2(x - 1)^2 - 5\)
Curve Q is a reflection in the \(y\)-axis of curve P.
Work out the equation of curve Q.
Give your answer in the form \(\quad y = ax^2 + bx + c \quad\) where \(a\), \(b\) and \(c\) are integers. [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(2(-x - 1)^2 - 5\) | M1 | oe Replacing \(x\) with \(-x\) |
| \(2(x^2 + x + x + 1) - 5\) or \(2x^2 + 4x + 2 - 5\) or \(2x^2 + 4x - 3\) | M1dep | oe expansion |
| \(y = 2x^2 + 4x - 3\) | A1 | |
| Alternative method 2 | ||
| \(2(x^2 - x - x + 1) - 5\) or \(2x^2 - 4x + 2 - 5\) or \(2x^2 - 4x - 3\) | M1 | oe expansion Multiplying out original expression |
| \(2(-x)^2 - 4(-x) - 3\) or \(2x^2 + 4x - 3\) | M1dep | oe Replacing \(x\) with \(-x\) |
| \(y = 2x^2 + 4x - 3\) | A1 | |
Additional guidance
| Using symmetry in \(y\) axis, \(y = 2(x + 1)^2 - 5 \;\rightarrow\; y = 2x^2 + 4x - 3\) | M1M1A1 |