1 of 8 0-day streak

Analyse and optimise a quadratic model

Question 1 of 8

Calculator allowed

A model for a moving platform uses \(t\) for time after the start. The model output is vertical position, measured in metres

y=\frac{1}{2}(t-4)^2 + 22

The meaningful domain is \(3\le t\le 8\), where t is measured in seconds

The output level \(\frac{45}{2}\) metres is used for the threshold question

(a)2 marks

What is the exact turning-point coordinate pair for this physical model?

\(x_v\) \(y_v\)

(b)1 mark

Choose whether the turning point gives the largest or smallest model output

The turning point gives a minimum output

The turning point gives a maximum output

Where does the smallest allowed vertical position occur?

Use the turning point

Use the right domain endpoint

Use the left domain endpoint

(d)1 mark

Give the smaller input that reaches \(\frac{45}{2}\) metres as an exact value

\(x_1\) (s)

(e)1 mark

Give the larger input that reaches \(\frac{45}{2}\) metres as an exact value

\(x_2\) (s)