A drone’s height $y$ metres at horizontal distance $x$ metres is modelled by \(y=12+7x-\frac12x^

Question

A drone’s height $y$ metres at horizontal distance $x$ metres is modelled by $y=12+7x-\frac12x^2$, for $0\le x\le14$. The table gives values for the model. Find $p$. Draw the graph on the supplied grid. State the coordinates of the turning point and the equation of the line of symmetry. State whether the turning point is a maximum or a minimum. Explain using the shape of the graph. At the boundary $x=12$, a cable is 30 m above the ground. State whether the drone is above or below the cable and find their vertical separation. $\text{Distance (m)}$ $\text{Height (m)}$

Accepted Answer

(a) $p=32$. (b) See worked solution. (c) $(7,36.5)$, $x=7$. (d) Maximum; the graph opens downwards. (e) Below by 6 m.

A quadratic model

A quadratic model

Solution:

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