Quadratics By Arnav

Everything you need to know, about Quadratics.

Table Of Contents

1.Intro and Terms you will need to know

2.What is Quadratics

3.Difference between Linear and Non Linear

4.Vertex Form and Graphing it

5.Finding Equation and Vertex Form

6.Factored Form

7.Binomials? What are they?

8.Multiplying Binomials

9.Common Factors and Simple grouping

10.Factoring by Grouping

11.Factoring Trinomials

12.Factoring Special Trinomials

13.Squared?

14.Completing the Square

15.Quadratic Formula? What is it?

16.Solving from Vertex Form

18.Quadratic Formula + Discriminant

19.Word Problems

20.Conclusion

Intro and Terms you will need to know

FACING UP AND DOWN PARABOLA

- If equation is negative, parabola will be facing downwards with a maximum point. If parabola is positive, it will be facing upwards with a minimum point.

X-INTERCEPT

- Where the point crosses on the x axis

VERTEX

- The point the parabola starts from

AXIS OF SYMMETRY

- The x coordinate of the vertex

OPTIMAL VALUE

- The y-coordinate of the vertex. The highest or lowest point. May also be the vertex.

What is Quadratics?

Quadratics means quadratic relationships. "Quad" means squared. Which means an exponent of 2 or a number needs to be squared in order to be a quadratic relation.

Difference between Linear and Non Linear Relations

Vertex Form and Graphing it

y = a(x - h)2 + k, where (h, k) is the vertex of the parabola. In y = a(x - h)2 + k, a effects the vertical stretch, h affects the horizontal stretch, k affects the vertical stretch and if a is negative there will be a reflection.

Finding Equation and Analyzing Vertex form

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Factored Form

In General, if y=a(x-r)(x-s)


The zeroes are found by setting each "factor" equal to zero


So: x-r =0 means x=r and x-s=0 means x=s


Axis of symmetry is midpoint of the two zeroes so x=r+s/2


The optimal value is found by subbing the axis of symmetry value into the equation.

What are Binomials?

Binomials are an algebraic expression of the sum or the difference of two terms. For Example, 7x + 2 is a binomial.

Multiplying Binomials

Vertex Form to Standard Form


Video at : https://www.youtube.com/watch?v=kCG0ZvMZzjI

Multiplying binomials

Common Factors and Simple Grouping

Factoring will take us from Standard Form back to Factored Form


Video at : https://www.youtube.com/watch?v=l8gU7G1rhJg

Common factors snd simple grouping
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Factoring By Grouping

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Factoring Trinomials

Factoring will take us from Standard Form back to Factored Form
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Factoring Special Trinomials

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What does "SQUARED" mean?

Squared means a number multiplied by it self. For example, the squared of 6 would be 6^2. It would be 6 x 6 = 36. So, 6^2 would equal 36.

Completing The Square

This is how you get standard form into vertex form.
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What is the Quadratic Formula?

It helps us to find the the two x - intercepts
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Solving From Vertex Form

Solving from vertex form
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Quadratic Formula + Discriminant

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Word Problems

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Conclusion

This website was made to teach what Quadratics is. This website will teach you how to do many things in Quadratics. It will teach you how to factor, isolate, many formulas and much more. This website will help many in their future :)