IB Maths AI HL Sl 1 8 Technology for Equations Questions

Practise using technology to solve systems and equations, selecting valid domain roots, checking by substitution or graphs and interpreting the model result.

Exam points

Use graphing or numerical technology to solve systems of up to three linear equations and state the unique solution with appropriate precision.
Use technology to solve polynomial or other permitted equations, identifying roots or zeros and selecting those in the stated domain.
Interpret a technology-generated solution in the model, rejecting invalid roots and checking the result by substitution, graph behaviour or contextual constraints.

[Maximum number: 3]

A sports player on a horizontal athletic field hits a ball. The height of the ball above the field, in metres, after it is hit can be modelled using a quadratic function of the form $f(x)=a x^{2}+b x+c$ , where x represents the horizontal distance, in metres, that the ball has travelled from the player.
A specialized camera tracks the initial path of the ball after it is hit by the player. The camera records that the ball travels through the three points (3,2.36),(10,5) and (17,7.16), as shown in Diagram 1.

Diagram 1

Use your answer to part (a) and two similar equations to find the equation of the quadratic model for the height of the ball.

finding other equations to solve simultaneously
$5=a(10)^{2}+b(10)+c$ AND 7.16 $=a(17)^{2}+b(17)+c$
OR 5=100 a+10 b+c AND 7.16 =289 a+17 b+c
any one coefficient in equation correct
$f(x)=-0.00490 x^{2}+0.441 x+1.08$ $\left(f(x)=-0.00489795 \ldots x^{2}+0.440816 \ldots x+1.08163 \ldots\right)$ $\left(f(x)=-\frac{6}{1225} x^{2}+\frac{108}{245} x+\frac{53}{49}\right)$
Note: Award at most (M1)(A1)A0 if answer is not expressed as an equation.

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IB Maths AI HL Sl 1 8 Technology for Equations Questions question 1