Quadratic Relationships

By: Bikram Dhaliwal

What is a Quadratic relation?

A quadratic relation is the involvement of relations of unknown quantity and variables

1st difference and 2nd difference

1st difference and 2nd difference is when you have a chart of numbers and if the second line of numbers have the same difference of numbers in between them it is linear or called 1st difference. But if the second row of numbers does not match you go to the next row of differences and find the difference between them it they all match its called a quadratic or 2nd difference. If the numbers still do not match it is called neither.
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1 Transformation

The -H moves left and right when the H is positive the vertex moves left, when the H is negative the vertex moves right.

2 Transformation

The K value moves up and down when the K is positive the vertex moves up, when the K is negative the vertex moves down.

3 Transformation

The A value stretches the parabola on the x intercept.

Word problem using vertex form

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Summary Of The Vertex Form

What is the purpose of vertex form?

  • Tells you if the parabola is stretched or compressed
  • You can find out if it opens up or down
  • Tells you the vertex

What does H value mean?

  • Tells you the x value of the vertex

What does K value mean?

  • Tells you the y value of the vertex
  • If the value is positive the vertex moves up
  • If the value is negative the vertex moves down


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Setting Up vertex form word problem youtube

Vertex Form Word Problem (Video)

Vertex Form Word Problem

Graphing Using Transformations (Video)

Graphing Quadratic Transformations (Grade 10 academic Lesson 4.4).mov


"Graphing Quadratic Transformations (Grade 10 Academic Lesson 4.4).mov."YouTube. N.p., n.d. Web. 18 Mar. 2016.

"Graphing Quadratic Equations." N.p., n.d. Web.

"Vertex+form - Google Search." Vertex+form - Google Search. N.p., n.d. Web. 18 Mar. 2016.

"DIGI 203 Algebra 1 - Graphing a Quadratic Function in Vertex Form." DIGI 203 Algebra 1 - Graphing a Quadratic Function in Vertex Form. N.p., n.d. Web. 18 Mar. 2016.

Learning goals

I found out how to find vertex form

I learned how to graph vertex form

I learned 1st differences and 2nd differences

Part #2

Factored form

The form of an algebraic expression in which no part of the expression can be made simpler by pulling out a common factor.

ex. The factored form of the expression x2+x-2 is (x+2)(x-1).

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Common Factors

The highest number that divides exactly into two or more numbers.

When we find all the factors of two or more numbers, and some factors are the same ("common"), then the largest of those common factors is the Greatest Common Factor.

Abbreviated "GCF". Also called "Highest Common Factor"

Example: the GCF of 12 and 16 is 4, because 1, 2 and 4 are common factors of both 12 and 16, and 4 is the greatest.
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Graphing factored form

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Converting factored form to standerd form

Multiplying Polynomials

  • multiply each term in one polynomial by each term in the other polynomial
  • add those answers together, and simplify if needed
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Special Products


=(x+2)(x+2) and then just solve it like a regular polynomial

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Factor quadratic expressions of the form x2+bx+c

Here are the steps to factoring a trinomial of the form x 2 + bx + c , with c > 0 . We assume that the coefficients are integers, and that we want to factor into binomials with integer coefficients.

  1. Write out all the pairs of numbers which can be multiplied to produce c .
  2. Add each pair of numbers to find a pair that produce b when added. Call the numbers in this pair d and e .
  3. If b > 0 , then the factored form of the trinomial is (x + d )(x + e) . If b< 0 , then the factored form of the trinomial is (x - d )(x - e) .
  4. Check: The binomials, when multiplied, should equal the original trinomial.
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Factor Quadratic Expression of the Form ax2+bx+c

How to Factor Trinomials ax^2+bx+c.

Factoring a perfect square

Factoring Perfect Square Trinomials - Ex1

Word Problem

More Word Problems Using Quadratic Equations - Example 1

Learning Goals

I learned how to multiply polynomials.

I learned what special products are.

I learned how to factor a perfect square.

Part 3

Chapter 6

In chapter there is not that many lessons but there are a few one of them is maxima and minima, Solving Quadratic Equations, Graphing Quadratics Using the x-Intercepts, The Quadratic Formula, Solving Problems Using Quadratic Equations.
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Maxima and Minima

Example: A ball is thrown in the air. Its height at any time t is given by:

h = 3 + 14t − 5t2

What is its maximum height?

h = 0 + 14 − 5(2t)
= 14 − 10t

Now find when the slope is zero:

14 − 10t = 0

10t = 14

t = 14 / 10 = 1.4

The slope is zero at t = 1.4 seconds

And the height at that time is:

h = 3 + 14×1.4 − 5×1.42

h = 3 + 19.6 − 9.8 = 12.8

And so:

The maximum height is 12.8 m (at t = 1.4 s)

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Completing the square

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This is one of the most simple part of the unit all you have to do is get the equation find the half of the number and then square it so if its 10 it would be 5^2 and then write +5^2 and then -5^2 then just keep the same number from the back and all you have to do is solve so 5^2 would be 25 so -25 plus the last number which will give you the K and then the H you will get when you just take half of the 10 which is 5 and then you get your 2 Points

Solving Quadratic Equations

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The picture above is a picture of a quadratic equation fully solved. To solve all you have to do is sub in the numbers so it is useful if you will already label A B C and then it will be more easy to know where the number is going. After that step is done all you have to do is just solve and then you will be done with the quadratic equation.

Word Problems Using Quadratic Formula

More Word Problems Using Quadratic Equations - Example 1

More Word Problems

How to Solve Word Problems Using Quadratic Equations

My Video



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This was one of my best tests ever i got really good and i did really good on all the completing the square questions. With this test i also learned that practice equals perfect i tried very hard on this test and i leaned that i cant just get good on tests because of luck i actually have to practice. Just like the quote " The harder I work the luckier I get" - Thomas Jefferson. The connections I think there are is that you can't do the next unit without learning the one before cause they all relate to each other and one you learn one you have to build almost like a pyrimid and then you will reach success cause if you don't have a base the top can't stay up. Like how the quadratic formula gives you points to graph so you need to know the quadratic formula and connect it to graphing so it's all like a pyramid.

Learning Goals

Graphing Quadratics using the x-intercept

Solving Quadratic Equations

Maxima and Minima