IB Mathematics Applications & Interpretation Question Type 3: Converting Between Different Forms Exercises

Convert the quadratic function $f(x)=2x^2-8x+5$ from its standard form to vertex form.

Express the complex number $5(\cos 60^{\circ }+i\sin 60^{\circ })$ in rectangular form $a+bi$.

Express ${\log }_3(x-4)=2$ in its exponential form.

Write the equation $2^x=8$ in logarithmic form.

Convert the repeating decimal $0.\overline{36}$ to a fraction in simplest form.

Convert the line $y-3=2(x+1)$ into standard form $Ax+By+C=0$.

Convert the complex number $-2+2i$ to polar form $r(\cos \theta +i\sin \theta )$ with $0\le \theta <2\pi$.

Factorise the quadratic $h(x)=x^2-5x+6$.

Given the parametric equations $x=1+2t$, $y=3t-1$, eliminate the parameter and write $y$ as a function of $x$. [3 marks]

Convert the point $(3,-3)$ from rectangular coordinates to polar coordinates $(r,\theta )$ with $0\le \theta <2\pi$.

Expand the quadratic $g(x)=3(x+2{)}^2-7$ and write it in standard form.

Find the Cartesian coordinates of the point with polar coordinates $(4,150^{\circ })$.