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2022 EJC J1 MYE Q8 A curve $C$ has equation $y=frac{2{{x}^{2}}+5x-1}{x+3}$. (i) Using an algebraic method, determine the range of values that $y$ can take. [3] (ii) Sketch $C$, labelling
2022 TMJC J1 MYE Q2 A hyperbola has equation ${{y}^{2}}+2dy-{{x}^{2}}+2x=2-{{d}^{2}}$, where $d$ is a real constant. (i) Show that the equation of the hyperbola can be expressed as ${{left( y+d
2022 TJC J1 MYE Q11 (b) The curve ${{C}_{1}}$ has equation ${{x}^{2}}-2x-4{{y}^{2}}=0$. (i) Sketch the graph of ${{C}_{1}}$, stating clearly the coordinates of any points of intersection with the axes
2022 CJC J1 MYE Q3 A curve $C$ has equation ${{left( x-3 right)}^{2}}+4{{left( y+1 right)}^{2}}=4$. (i) Sketch $C$, indicating clearly the coordinates of the centre and the coordinates of the
2010 NJC Promo Q6 Sketch the graph of $y=frac{2}{xleft( x-mu right)}$, where $mu $ is a positive constant, indicating clearly any axial intercept(s), asymptote(s) and coordinates of turning point(s). Given
NJC Graphing Techniques Tutorial Q5 The curve $C$ is the translation of $frac{{{x}^{2}}}{9}-{{y}^{2}}=1$ by one unit in the positive $x$-direction. (i) Sketch the curve $C$, showing clearly the equations of
NJC Graphing Techniques Tutorial Q4 The diagram below shows the graph of the function $y=text{f}left( x right)$, where $text{f}left( x right)=frac{a{{x}^{2}}+bx+c+2}{x+d}$ and $a$, $b$, $c$ and $d$ are integer constants.
Graphing Techniques Tutorial Q1 A curve $C$ has equation ${{y}^{2}}=4aleft( a-x right)$ for some positive constant $a$. (i) Describe a sequence of transformations that map ${{y}^{2}}=x$ to $C$, giving your
2022 RI Promo Q7 (a) Sketch on the same diagram the graphs of $y=left| x-1 right|$ and $y={{x}^{2}}-3$.Hence solve the inequality $left| x-1 right|<{{x}^{2}}-3$. [3] (b) A curve $C$ has
2022 ACJC Promo Q3 The curve $C$ with equation $y=frac{a{{x}^{2}}+bx+c}{3x+1}$ passes through the point with coordinates $left( -1,-4 right)$ and has a turning point at $left( -3,-2 right)$. (i) Find