1 of 8 0-day streak

Analyse and optimise a quadratic model

Question 1 of 8

Calculator allowed

A model for a sensor calibration uses \(u\) for calibration setting. The model output is distance from a reference line, measured in millimetres

y=\frac{1}{2}(u+2)^2 + 30

The meaningful domain is \(-6\le u\le 0\), where u is measured in millimetres

The output level \(\frac{265}{8}\) millimetres is used for the threshold question

(a)2 marks

State the exact coordinates of the turn, with the input first

\(x_v\) \(y_v\)

(b)1 mark

Select the correct maximum-or-minimum description of the turn

The turning point gives a minimum output

The turning point gives a maximum output

Where does the smallest allowed distance from a reference line occur?

Use the right domain endpoint

Use the left domain endpoint

Use the turning point

(d)1 mark

Give the relevant input that reaches \(\frac{265}{8}\) millimetres as an exact value

\(u\) (mm)

Format: Exact value