Quadratics Top 10 Must Knows (ultimate study guide)

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0:00 - What is a Quadratic Relationship
2:09 - Standard Form
3:53 - Vertex Form
7:01 - Factored Form
9:33 - Factoring
12:18 - Solving by Factoring
14:37 - Solving by Completing the Square
16:17 - Quadratic formula
18:32 - The Discriminant
20:41 - 3 Ways to Find the Vertex

[maheshchavan]

This is the most clear video I've ever seen on quadratic

[sandhyaprabhu]

Oh my God. Love you, I wish you were my Maths teacher at college. Every student deserves a teacher like you🙏🙏

[abrahamhadish]

You are top one, who is enhancing my maths fulfillment.

[PotatoSinghTherd]

I love these videos! Keep up the good work.

[OmarFaruque-iq]

Damn! This dude teaches something in 30 mins that'd take professors hours!

[mimoali-mryd]

[00:00] The top 10 things to know about quadratics
- Quadratic relationships can be recognized from equations, tables, and graphs
- Quadratic relationships have a degree 2 polynomial equation and form a parabola shape
- All parabolas have a vertex and are symmetrical about a vertical axis
- The standard form equation of a quadratic is y=ax^2+bx+c
- From the standard form equation, we can determine properties of the quadratic relationship

[02:33] Understanding the basics of quadratic equations in standard and vertex form
- Standard form equation: a determines direction of opening, C reveals Y-intercept
- Table of values can be used to graph standard form equations
- Vertex form equation: H and K values determine vertex coordinates, a determines direction of opening
- Converting standard form to vertex form can help find vertex of Parabola

[05:08] The video explains the three forms of quadratic equations and their significance in solving and graphing quadratic functions.
- The standard form is ax^2 + bx + c and can be used to find the vertex, axis of symmetry, and intercepts
- The vertex form is a(x-h)^2 + k and can be used to find the vertex and axis of symmetry
- The factored form is a(x-m)(x-n) and can be used to find the x-intercepts

[07:40] Factored form basics of quadratics: finding X-intercepts, axis of symmetry, and vertex
- X-intercepts can be found by setting Y to zero and using the zero product rule
- Axis of symmetry is the average of X-intercepts
- Vertex falls on the axis of symmetry and can be found by substituting the X-coordinate into the factored form equation
- Quadratics with leading coefficient of one can be factored using product and sum method

[10:14] Learn how to factor and solve quadratic equations using factoring, including the difference of squares rule.

[12:47] The video explains how to solve quadratic equations by factoring and completing the square
- To factor a quadratic, find numbers that multiply to C and add to B, then use the zero product rule to find the roots
- If factoring is not possible, convert the quadratic to vertex form by completing the square, then rearrange to isolate X

[15:21] Learn how to solve quadratic equations using completing the square and the quadratic formula.
- Completing the square involves rearranging the equation to isolate X
- Quadratic formula is x = (-b ± sqrt(b^2 - 4ac)) / 2a
- Quadratic formula can be used to find solutions without completing the square
- Example: x^2 - 6x + 8 = 0 can be solved using quadratic formula to get x = 3 ± sqrt(17)

[17:55] Quadratic formula and discriminant determine the number and type of solutions to a quadratic equation
- Discriminant is the part under the square root in quadratic formula
- If discriminant is greater than zero, there are two real solutions
- If discriminant is equal to zero, there is only one real solution
- If discriminant is less than zero, there are no real solutions
- If discriminant is a perfect square, the quadratic is factorable

[20:28] The video explains three ways to find the vertex of a parabola in standard form
- Completing the square method involves factoring and adding/subtracting a constant
- Finding X-intercepts and averaging them gives the X-coordinate of the vertex
- Using the formula B/2A gives the X-coordinate, which can be used to find the Y-coordinate

[torianobess]

you could also use the identity (x+h) square - h squared = x squared + 2hx to complete the square.

[Limitless-learner]

Sir pls continue this series 🙏🏻 pls sir

[mosshead_vinsmoke]

Please do this to all general topics in Maths - trigo, geometry, PnC, Calc-1/2, Lin Alg, Disc Math....

[sammer-samm-]

Method 1)
(- x= 3) equation is given
Multiplying both sides by (-1)
-1*-x=-1*3
Then x=-3
or

Method 2)
Let the equation be (- x= 3)

If we multiply both sides with "MINUS" sign
-(- x)= -(3)
Then x= -3.
Which one is correct or both methods are correct .
Please help 🙏🙏

[judekirkcruz]

Holy shit I learned a lot more in this video than in my high school years!!

[rainyee-pclf]

6:55 the x coordinate of the vertex is supposed to written as -5, right?

[Big_Ray]

Now
How do we apply quadratic in solving real life problems?

[AerialAnomaly]

I have a unit test in about 2 hours, so I gotta lock in

[arosalesmusic]

The min or max can be found by taking F´(x) = 0

[davidbrown]

For your visually impaired viewers, please avoid that dark pink as it is hard for visually impaired people like myself to read against the dark background of the blackboard.

[kolmst]

1:21 ??? Please explain why this is happening? How can the difference of their differences all be the same? ????

[delegatedgamer]

Hi could you make video on book name cengage maths

[WhyPLL]

I’m in grade 7 and I can barely understand 😢

[radzelimohdramli]

one more way to find vertex by using differentiation method