[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
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.
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 🙏🙏
idk about these random people in youtube going about how they can understand every equation ever at like 9 year old, but i was only taught quadratic equations with factoring and completing the square in 8th grade and quadratic formula in 9th grade
Oh my God. Love you, I wish you were my Maths teacher at college. Every student deserves a teacher like you🙏🙏
[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
comprehensive and concise. thank you.
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.
Precise and informative 👌
I love these videos! Keep up the good work.
Please do this to all general topics in Maths - trigo, geometry, PnC , Calc-1/2 , Lin Alg , Disc Math....
Brilliant but does he have a bus to catch. He barely catches his breath. FAR TOO FAST .
The min or max can be found by taking F´(x) = 0
This is the most clear video I've ever seen on quadratic
THE BEST!!!
Sir pls continue this series 🙏🏻 pls sir
Too good sir.. thanks a lot😊
nice and clear thanks...
you could also use the identity (x+h) square - h squared = x squared + 2hx to complete the square.
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 🙏🙏
-1 can be written as "-",these both are correct
one more way to find vertex by using differentiation method
Very good
I already know how to solve quadratics
Then why are you here
I have a unit test in about 2 hours, so I gotta lock in
Now
How do we apply quadratic in solving real life problems?
Thanks
8 th grader understood everything 😮
Hi could you make video on book name cengage maths
Holy shit I learned a lot more in this video than in my high school years!!
I’m in grade 7 and I can barely understand 😢
You’ll get it nice cubing btw
How
How old r u in 7th grade?
idk about these random people in youtube going about how they can understand every equation ever at like 9 year old, but i was only taught quadratic equations with factoring and completing the square in 8th grade and quadratic formula in 9th grade
I learnt quadratics in year 8 so its fine if you dont understand in year 7
Nice mathematics thanks
thank you!
Which row is this?
Man I love this series
TYSMM
nice
just in time no way