By: Raghib khadaroo


The way you graph quadratics are similar to graphing any linear system except its a curved line which is referred to as a parabola. It is basically a way to graph curves to show when things are dropping off like if you were to graph the tragectory of you throwing a baseball on paper you would need a quadratic equation.



Parabolas are the curved lines formed from your x-intercepts and goes through the vertex, The line that splits it down the middle is called the axis of symmetry

Quadratic functions

  1. So, given a quadratic function, y = ax2 + bx + c, when "a" is positive, the parabola opens upward and the vertex is the minimum value. On the other hand, if "a" is negative, the graph opens downward and the vertex is the maximum value.

Analyzing Quadratics

To analyze a qudratic formula you must figure out the following

  • Find the x-intercepts
  • Find the Vertex

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Graphing vertex form

vertex form gives us the vertex and tells use either if it opens up or down knowing this makes it easier.


Either way works and will get you the same answer

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❤² How to Find the Vertex of a Parabola (mathbff)
(a) determines whether the parabola opens up or down that being determined whether it is positive or negative as for the vertex it is already giving to you in vertex form being (h),(k) which give your the x and y coordinates

Factoring trinomials

Factoring trinomials are quite complicated and will take practice before you can master the 3 most common methods to factor. The first method would have to be completing the square, second method is finding common factors and the lat method would have to be using square roots

Completing the Square

❤² How to Solve By Completing the Square (mathbff)

Using common factors

Using common factors is one of the easiest methods but can sometimes take you the most amount of time but all you need to remember is
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=x^2+7x+10 now we must find two numbers that multiply to 10 but add to 7

which is easy as the answer is 2 and 5 because: 2*5=10 2+5=7

they then become your new brackets


❤² How to Solve Quadratic Equations By Factoring (mathbff)

Using square roots

This method requires you to square root you (ax) and your (c) then add them and times by 2 to get your (bx) which means you got it right in which you can now fill in your brackets.

Quadratic Formula

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The quadratic formula is used to find the x-intercepts while in standard form (ax^2+bx+c) and is very easy to use once you have it memorized all you have to do is sub in the standard form into the equation and you'll get the right answer.

Revenue problems

Revenue problems are quite simple as you only need to follow the formula (price)(# of) to figure out your revenue. Lets say that my price is 5$ and i have 10 people and i say that for every 2 increase in price the number of people decrease by 2.

So then we write are let statement let x rep the # of 2 dollar increases

Revenue=(5+2x)(10-2x) then you solve for x