Is there anyway that I could learn the different types of graphs such as parabola, quadratic etc. and how to identify what types of graph an equation would be, including all types of equations,...

Is there anyway that I could learn the different types of graphs such as parabola, quadratic etc. and how to identify what types of graph an equation would be, including all types of equations, division, cubed, squared and so on?

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durbanville | High School Teacher | (Level 2) Educator Emeritus

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When identifying graphs, always look at the equation as this will help you. The equation indicates how many "x-es" there are; for example if `x^2` ` ` is the highest value of x, this indicates a parabola because x has 2 values; `x^3`  would be a cubic graph as it has 3 x-values, and so on.  A straight line has only one x value because it only touches the x-axis once so it will be `x^1` (ie. ` ` `(x)` as the highest x-value. In an exponential graph, x is the power (eg. `y=2^x` ).

The standard form of the equations, then gives you the clue:

Straight line or linear: `y= mx+b`  or `y=mx+c ` where m = gradient and  b or c represent the value of the y-intercept (where x=0)

Parabola / Quadratic: `f(x) = ax^2 +c` or `f(x) = ax^2+bx+c` . There is also the form `f(x) =a(x-h)^2 +k` where h is the x turning point and k is the y turning point.  We say `f(x)` because often, in a question, there is more than one graph,  and calling each one `y=`  can be confusing. Therefore, each graph is identified as, for example, `f(x)` , `g(x)` , and so on but essentially, `f(x) =` ... is the same as `y=` ...  

Hyperbola: `xy=k` or  `y=k/x`  or `y= k/(x+p) +q`   where p and q are the x and y asymptotes. There is a rectangular hyperbola but we will not cover that here.

Exponential: `y=a^x`  or `y=a^x+b` when the graph is translated.

Circle: `r^2=x^2+y^2` or `r^2= (x-a)^2 +(y-b)^2`

The first circle equation is when the center of the circle is at (0;0) and the values of a and b in the 2nd equation are the center of the circle when it is not at the origin.

Cubic: `y=ax^3 + bx^2 + cx + d` There are other variations from which it will be evident that there are 3 x-values.   

The notation may vary slightly in any of these descriptions. This is a basic explanation of the fundamental equations some of which do have restrictions. However, do not be overwhelmed by information. The more you practice, the more the equations will become familiar to you. 

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