IB Maths AA HL 2.6 Quadratic functions and parameter analysis Question Bank

Practise IB Maths AA HL 2.6 by analysing parameterised quadratics, discriminants and extrema in applied models.

Exam points

Use discriminants, roots and vertex conditions to derive parameter restrictions.
Analyse how changing a parameter alters the graph, number of roots or extremum.
Evaluate a quadratic model by checking domain, units and the meaning of each branch.

[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 SL 2.6—Quadratic functions 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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SL 2.6—Quadratic functions question 1