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Study SL 2.6—Quadratic functions conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

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A particle P moves along the x-axis. The velocity of P is $v \mathrm{~m} \mathrm{~s}^{-1}$ at time t seconds, where $v(t)=4+4 t-3 t^{2}$ for $0 \leq t \leq 3$ . When t=0, P is at the origin O .

Sketch a graph of v against t, clearly showing any points of intersection with the axes.

valid approach to solve $4+4 t-3 t^{2}=0$ (may be seen in part (a))
(2-t)(2+3 t) OR $\frac{-4 \pm \sqrt{16+48}}{-6}$
correct x - intercept on the graph at t=2
correct domain from 0 to 3 starting at (0,4)
vertex in approximately correct place for $t=\frac{2}{3}$ and v>4

Figure for Answer to Question 1 — IB Maths AA HL

Note: The following two A marks may only be awarded if the shape is a concave down parabola. These two marks are independent of each other and the (M1).
Note: The 3 must be clearly indicated.

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IB Maths AA HL Sl 2 6 Quadratic Functions Topic Practice

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Question 1