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Quadratics Part 1

1) Intro to Quadratics

2) Different parts of a Parabola

  • Axis of Symmetry
  • (x)Optimal Value (y)
  • Zeros
  • Vertex
  • y-intercept

3)Vertex Form.

Graphing Vertex Form

4) Finding the Equation and Analyzing

Vertex Form

5) Factored Form → y= a(x-r)(x-s).

Quadratics Part 2

1) Factoring Complex Trinomials

2) Factoring Simple Trinomials

3) Factoring Perfect of Squares

4) Factoring Difference of Squares

5) Factoring common factors

6) Expand and simplify .

7)Graphing Quadratics using x-intercept.

Quadratics Part 3

1) Completing the Square.

2) Quadratic Formula

3) Discriminant Formula

1) Intro to Quadratics.

Quadratics is solving in different ways. Whether it is solving or expanding, we have several methods that we can us to help us get an answer.

Different parts of a Parabola

As you can see there is a graph below that shows what different parts of a Parabola their is.


1) vertex -that is the point of the parabola at its maximum (max) or minimum (min) value

2)Axis of symmetry- it divides the parabola into 2 equal half's

3)Optimal Value- the the y co-ordinate of the vertex

4) Zero- it can be called a (zero/x-intercepts/roots) is when the graph goes though the x axis

5)y-intercept is a parabola is where the graph crosses the y-axis

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Graphing Vertex Form

There a little of information for graphing a vertex form.

This is a vertex with a positive equation

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Are some things that you have to remember when you are graphing a vertex form:

-Vertical transformation is a (something #) of a unit that opens up or down

-Horizontal transformation is a (something #) of a unit that moves left or right

-a number that is factored by a vertical or compressed

Finding the Equation and Analyzing Vertex Form.

To start off with is the form Analyzing Vertex Form without any valuables.


The 2 beside the the power of 2 for example The vertex of a Parabola is (-2,2) and the x-intercept is (2,4). What is the equation of the of the parabola.

1) Write the equation down y=a(x-h)^2+k

2) Fill n the valuable in the equation 4=a(2+2)^2+23)

3) than you would have to do the brackets 4=a(2+2)^2+24)

4)than you would have to do the power of 2 4=a(4)^2+25)

5) than do take away the 2 and do it to the other side too 4=a(16)+26)

6)than divide the the 2 side by 2 2=16a =7)2/2=16/28) a=8

Therefor the equation will be y=8(x+2)^2=2

Factored Form

Factored form- y=(x+r)(x-s)The x-intercept are simply just l zeros in factored form are written as Example of how we get the zeros in factored form.Example: y=(x+2)(x-6)0=(x+2)(x-6)0=x+2 → -2=x → Therefore one zero is 20=x-6 → 6=x → Therefore one zero is 6

Quadratics Part 2

Factoring Complex Trinomials

There is a video that tells you how to solve Factoring Complex Trinomials.
Grade 10 Quadratics- Complex Trinomal's

Factoring Simple Trinomials

There is a video that tells you how to solve Factoring Simple Trinomials.
Grade 10 Quadratics- Simple Trinomial's
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Factoring Perfect of Squares

There is a video that tells you how to solve Factoring perfect of squares.
Grade 10 Quadratics-Perfect Squares

Factoring Difference of Squares

There is a video that tells you how to solve Factoring difference of squares.
Grade 10 Quadratics- Difference of Squares

Factoring common factors

There is a video that tells you how to solve Factoring common factors.
Grade 10 quadratics- common factoring
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Expand and simplify

There is a video that will tell you how to expand and simplify
Grade 10 Quadratics- Expanding and Simplifying

Graphing Quadratics using x-intercept

There is a video that will show you how to graphing Quadratics using x-intercept
0.2 Graphing with Intercepts

Quadratics Part 3

Completing the Square

This is the equation to start of with y=x^2-10+20

1) First you have to take the # on the right side out y=(x^2-10)+20

2) Now you want to see the middle # that is 10, you have to divide the by 2 and the square root it to 2. 10/2= 5 52=25

3) Now you would add the 25 in and subtract 20 too. y=(x^2-10+25-25)+20

4)After you have to take out the -25 in the brackets and put beside the 20. y=(x^2-10+)+20-25

5)Now you have to subtract the 20-25 so that would be -5.(x^2-10+)-5

6)Lastly. you would have to see want you can divide with 1x. it will be 1 and 1. Also you would have to find a # that will add to the middle number and that will multiply to the last number. (x+5)^2-5

Quadratic Formula + standard Formula

This is the formula of solving quadratic to standard form.
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3 15 Quadratic Formula

Discriminant Formula

This pretty easy because it doesn't have lot of steps.
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1) 6^2-4(1)(6)

2) 36- 24

3) =12


The Quadratics unit, I feel that I have learned a lot and like how to solve different types of equations. It s was pretty fun learning the competing the square because it was easy and interesting way of a short cut intend of doing the quadratic formula. The quadratic unit was hard but it was helpful. This quadratics unit was the different than the last years math. But overall the quadratic unit was good.