A curve is defined in parametric form by `x=2+t` and `y=3-2t^(2)` for `-1 <= t <= 0`.
Which diagram best represents this curve?
Functions, EXT1 F1 2002 HSC 1e
The variable point `(3t, 2t^2)` lies on a parabola.
Find the Cartesian equation for this parabola. (2 marks)
Functions, EXT1 F1 2003 HSC 1d
A curve has parametric equations `x = t/2, y = 3t^2`.
Find the Cartesian equation for this curve. (2 marks)
Functions, EXT1 F1 SM-Bank 9
- Sketch the graph of the function described by the parametric equations
`x = 4t - 7`
`y = 2t^2 + t` (2 marks)
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- State the domain and range of the function. (1 mark)
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Show Answers Only
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- `text(Domain: all)\ x`
`text(Range)\ {y: −1/8 <= y < ∞}`
Show Worked Solution
i. `x = 4t – 7 \ \ => \ \ t = (x + 7)/4`
| `y` | `= 2t^2 + t` |
| `y` | `= 2((x + 7)/4)^2 + ((x + 7)/4)` |
| `16y` | `= 2(x + 7)^2 + 4(x + 7)` |
| `16y` | `= 2x^2 + 28x + 98 + 4x + 28` |
| `16y` | `= 2x^2 + 32x + 126` |
| `8y` | `= x^2 + 16x + 63` |
| `y` | `= 1/8(x + 7)(x + 9)` |
`=>\ text(Equation is a concave up quadratic with)`
`text(zeros at)\ \ x = −9\ text(and)\ \ x = −7.`
ii. `text(Axis at)\ \ x = −8`
| `:.\ y_text(min)` | `= 1/8(−1)(1)` |
| `= −1/8` |
`text(Domain: all)\ x`
`text(Range:)\ −1/8 <= y < ∞`
Functions, EXT1 F1 SM-Bank 5
Find the Cartesian equation for the curve with the parametric equations
`x = 3t`
`y = 2t^2`. (1 mark)