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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.

IB Maths AI HL Sl 1 8 Technology for Equations Topic Practice

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IB Maths AI HL Sl 1 8 Technology for Equations Topic Practice

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Question 1