Non-Linear Relationships C

numberandalgebra path adv ext

Non-linear relationships C (Path) | NSW Curriculum Website

• MA5-NLI-P-01 interprets and compares non-linear relationships and their transformations, both algebraically and graphically

📖 Prior Knowledge

Content	Prior knowledge	Used for
Right-angled Triangles	- Pythagoras’ theorem	- equation of a circle
Equations C	- Factorising quadratics and completing the square	- sketching parabolas
Non-linear Relationships B	- Basic transformations of parabolas and exponentials	- further transformations of parabolas and exponentials
Variation and Rates of Change A	- hyperbolas in inverse variation	- transformations of hyperbolas

Graph parabolas and describe their features and transformations.pdf

• Use graphing applications to compare parabolas of the form $y=k{x}^2$,  $y=k{x}^2+c$, $y=k(x-b{)}^2$, and $y=k(x-b{)}^2+c$,  and describe their features and transformations
• Find $x$- and $y$-intercepts algebraically, where appropriate, for the graph of $y=a{x}^2+bx+c$, given $a$, $b$ and $c$
• Determine the equation of the axis of symmetry of a parabola using either the formula $x=\frac{-b}{2a}$ or the midpoint of the $x$-intercepts
• Find the coordinates of a parabola’s vertex using a variety of methods
• Graph quadratic relationships of the form $y=a{x}^2+bx+c$ identifying and applying features of parabolas and their equations without graphing software

Graph exponentials and describe their features and transformations.pdf

• Use graphing applications to graph exponential relationships of the form $y=k(a{)}^x+c$ and $y=k(a{)}^{-x}+c$ for integer values of $k$, $a$ and $c$ (where $a>0$ and $a\ne 1$), and compare and describe any relevant features

Graph hyperbolas and describe their features and transformations.pdf

• Use graphing applications to graph, compare and describe hyperbolic relationships of the form $y=\frac{k}{x}$ for integer values of $k$
• Use graphing applications to graph and describe a variety of hyperbolas, including where the equation is given in the form $y=\frac{k}{x}+c$ or $y=\frac{k}{x-b}$ for integer values of $k$, $b$ and $c$

Graph circles and describe their features and transformations.pdf

• Derive the equation of a circle $x^2+y^2=r^2$ with centre $(0,0)$ and radius $r$ using the distance formula
• Identify and describe equations that represent circles with centre at the origin and radius of the circle $r$
• Graph circles of the form $x^2+y^2=r^2$, where $r$ is the radius of the circle using graphing applications
• Establish the equation of the circle with centre $(a,b)$ and radius $r$, and graph equations of the form $(x-a{)}^2+(y-b{)}^2=r^2$
• Find the centre and radius of a circle with the equation in the form $x^2+y^2+ax+by+c=0$ by completing the square

Distinguish between different types of graphs by examining their algebraic and graphical representations and solve problems.pdf

• Identify and describe features of different types of graphs based on their equations
• Identify a possible equation from a graph and verify using graphing applications
• Find points where a line intersects with a parabola, hyperbola or circle, both graphically and algebraically

Graph and compare polynomial curves and describe their features and transformations.pdf

• Use graphing applications to graph and compare features of cubic equations of the form $y=a{x}^3+c$, where $a$ and $c$ are integers
• Use graphing applications to graph a variety of equations of the form $y=k{x}^n$, where $n$ is an integer and $n\ge 2$, and describe the effect on the shape of the curve where $n$ is an odd or an even number
• Use graphing applications to graph curves of the form $y=k{x}^n+c$ and $y=k(x-b{)}^n$ where $n$ is an integer and $n\ge 2$, and describe the transformations from $y=k{x}^n$