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 $5\bigl(\cos 60^\circ + i\sin 60^\circ\bigr)$ 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 $(4, 150^\circ)$.