Learning Grade 10 Quadratics

Sahra B

What are Quadratics ?

Have you ever wondered how roller coasters are made? Well, there is math behind it. Linear relations and parabolas are used to form a roller coaster. In Quadratics the word 'QUAD' means square (x²). The power to makes the quadratic have a curve in it.

First and Second differences

To know if your table is linear, quadratic or none we use table of values. You have to see the differences in the Y column, if it is a constant change when you subtract y2 - y1 then it is linear. If there is no constant then it be neither linear or quadratic.

First Differences and Second to see if Quadratic , Linear or Neither

First and second differences are used to see if it is a Quadratic or Linear relation. The first difference is the constant when you do Y2- Y1. If it is a constant value then its linear. Same thing with the second difference.

Investigating Vertex form

The vertex is the lowest or highest point of a parabola ( quadratic graph). To find its highest or lowest point you look at the minimum value (if graph opens upwards) or maximum value (if graph opens downwards)
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Graphing Vertex Form & analyzing

To graph the vertex form you have the formula Y=a(x-h)2+k


You plot the vertex which is (h,k)


And then you follow the steps pattern which is a,3a , 5a and etc.

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Converting Factored form to Standard form

Converting factored form (ex. y=a(x-r)(x-s) ) to standard form y=ax^2+bx+c


To convert into standard form you expand and simply.


Step 1 - Multiply the binomials

Step 2 - Collect like terms

Step 3 - Distribute 'a' value to result.

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Factoring by grouping & Common factoring

Polynomial form (4 terms) : ax^3+bx^2+cx+d


1. Find common factors for ax^3 , bx^2

2. Find common factors for cx+d

3. Put common factor outside of each bracket and put the remainder inside of bracket

4. Now you have to group, two brackets should have same number, and the common factors outside of bracket , group them.

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Finding x-interept by setting y=0

To find the x intercept of a quadratic equation by setting y as zero , you must ...


1) Set your Y as 0 and solve for x for each binomial

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Factoring trinomials with leading 1

Factoring from standard form back to factored form


We want our equation to go from ax^2+bx+c to y=a(x-r)(x-s)


1) Find any common factors

2) Find a number that multiplies to 'c' (aka last number) & adds to 'bx' (aka middle number)

3) Once those two numbers are chosen make two brackets both with 'x' as first number and the second number the numbers you had chosen.

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Factoring trinomials WITHOUT leading 1

Factoring a trinomial without a leading number that is 1 , which means that your first term will not just be 'x^2 ' it will be for eg. '6x^2' .


Our goal is to get it from standard form to factored form.


1) Find a common factor in your equation

2) Find two numbers that multiplies to last number (C)

3) Find two numbers that multiplies to first number (ax)

4) Cross multiply & if doesn't equal your sum then change the numbers around or find new numbers.

5) Group them

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Factoring special trinomials

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Standard form : y=ax^2+bx+c

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Getting your x intercepts from Quadratic formula.

2x^2+9x+6=0


a=2 b=9 c=6


Plug in the numbers in the quadratic formula & solve.

Axis of Symmetry


In order to find the axis of symmetry for a standard form equation you need to know your 'a' and 'b'.The formula to find axis of symmetry in standard form is -b/2a


Ex.Y=2x^2+8x+5

Our a is 2 and our b is 8.

-8

(2)(2)

A.O.S = -2

Optimal Value

Finding Optimal Value !

To find the optimal value all you need to do is replace the "x" in the equation with the A.O.S and then solve.

Y=2x^2+8x+5

Y=2(-2)^2+8(-2)+5

Y=2(4)-16+5
Y=8-16+5

Y=-3




My videos- Factoring

https://youtu.be/8p7dqHppu9E

https://youtu.be/pgCeKEGehqA

https://youtu.be/qG3iDXwGarg

https://youtu.be/eEvIUkvHDDc

https://youtu.be/xmF0OwI24d4

Reflection On Quadratics

The quadratic unit started off a bit challenging for me because I was not very good at parabolas , it was probably the most annoying thing ever. But when we started factoring, I started enjoying quadratics because I actually understood how to factor. Quadratics has been challenging and I have had my points where I just wanted to give up but then there was parts where I actually understood the concept of Quadratics and things got better.