The parabola `y = −2x^2 + 8x` and the line `y = 2x` intersect at the origin and at the point `A`.
Find the `x`-coordinate of the point `A`. (2 marks)
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| i. |
|
`x\text(-coordinate of)\ A:`
| `y` | `= 2x\ \ \ \ \ …\ text{(i)}` |
| `y` | `= -2x^2 + 8x\ \ \ \ \ …\ text{(ii)}` |
`text(Subst)\ y = 2x\ text{from (i) into (ii):}`
| `-2x^2 + 8x` | `= 2x` |
| `-2x^2 + 6x` | `= 0` |
| `-2x (x-3)` | `= 0` |
`:.\ x = 0\ text(or)\ 3`
`:.\ x\text(-coordinate of)\ A\ text(is 3)`