IB Maths AA HL Sl 2 6 Quadratic Functions Questions

Practise analysing parameterised quadratics with discriminants, roots and extrema, then checking domain, units and the meaning of each model branch.

Exam points

Solve and analyse quadratic functions using roots, vertex, discriminant and graph features.
Determine parameters, intersections or inequalities for quadratics using complete evidence.

[Maximum number: 4]

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 IB Maths AA HL Sl 2 6 Quadratic Functions Questions 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 Questions question 1