Complete the square and restrict the range

Practise complete the square and restrict the range with an original VectorPaths question, worked explanation and related VCE Methods practice.

4 practice marks

Original practice question

Let $f(x)=2x^2-8x+5$ for $0\leq x\leq5$. (a) Express f in completed-square form. [2 marks] (b) Find the turning point and range on the stated domain. [2 marks]

Worked explanation

• Part (a)

  $2(x^2-4x)+5=2[(x-2)^2-4]+5=2(x-2)^2-3$.

• Part (b)

  The minimum is $-3$ at $x=2$. Compare endpoint values $f(0)=5$ and $f(5)=15$ to obtain the maximum 15.

(a) $2(x-2)^2-3$.; (b) $(2,-3)$; $[-3,15]$.

Original VectorPaths practice; not an official VCAA question or marking rubric.