New Quadratics

The new and improved way to learn Quadratics

What to be prepared for

i have noticed that in this unit homework is key, participating is also really good. Do not be scared to ask a question. i personally noticed that i lack organization and lack of being attentive as well. so if your anything like me pay attention do homework and ask questions, i learned that a bit late.

Fustrated of Quadratics.

Now you can with this new interactive website. You will learn:

- Standard form Quadratics

- Vertex Form Quadratics

-Factored form Quadratics

_ Common, Simple, Complex, Perfect Squares and Difference of Squares Factoring

Standard Form Quadratic

y = a(x - h)2 + k what does this mean?

  • If a < 0, the quadratic will open downwards.
  • If a > 0, the quadratic will open upwards

If you increase the a value the arms will grow larger.

The (h,k) will always be the coordinates of the minimum and maximum values

The list on what to do.

New Topic Vertex form

What is Vertex form.

vertex form is y = a(x-h)² + k where (h,k) is the vertex of the parabola. video below and step by step work on right

Parabola

The Parabola is what happens to the graphing a Quadratic Relation- containing very important segments that come together to create a Parabola:

Vertex which is where the parabola and the axis of symmetry meet: (x,y)

Axis of Symmetry which divides the parabola equally: (x=#)

X-Intercept is also known as (zeroes/all real numbers) is where the line passes through the x axis: (#,0)

Y-Intercept where the line passes through the y axis: (0,#)

Optimal Value is the Y coordinate of the Vertex and the Optimal Value is also the highest or lowest point: (y=#)

❤² How to Find the Vertex of a Parabola (mathbff)

Factored form

on this there will be a video below on solving factored form

Factoring

There are a lot of ways to factor. factoring is only better when you see so there will be a verity of videos and pictures
❤² How to Solve Quadratic Equations By Factoring (mathbff)
Common Factoring Tutorial
Factoring Trinomials - MathHelp.com - Algebra Help
Factoring Complex Trinomials
Factoring Perfect Square Trinomials and Difference of Squares

Standard Form

Zeroes, Zeroes and more Zeroes

standard form you must first show the a,b and c once you are done that you then will plug in those number into this ax2 + bx + c = 0

Do not let the x confuse you its there to be figured out not multiply

Big image

Converting From form to form

Converting vertex form to factored form

To convert from Vertex form to factored form

1. Change y as 0

2. Place k value over the equal sign

3. Divide "a" value form both sides of equation

4. Square root both sides so you can get rid of the square root on the right side

5. Finally move your "h" value over the equal sign

Converting Standard form to vertex form

Changing from Standard form to Vertex form.

1. Remove the common factor from the x^2 and the x term(coefficient)

2. Locate the constant that must be added and subtracted to create a perfect square. Rewrite the expressions by adding and subtracting the constant

3. group the three terms that form the perfect square ( move subtracted value outside the brackets by multiplying it by the common factor fist )

4.factor the perfect square and collect all like terms

Zeroes

The graph of a quadratic function is a parabola. A parabola can cross the x-axis once, twice, or never. These points of intersection are called x-intercepts or zeros.

optimal value

Optimal" simply means best. Let's say you are using a parabola to define the cost of something as a function of some variable. In that case "optimal" would probably be the cheapest value, or the lowest point on the parabola. In other cases it could mean the maximum. Either way, it's the value that's somehow considered the best.

Axis of Symentry

Find the axis of symmetry of the parabola shown. The x-coordinate of the vertex is the equation of the axis of symmetry of the parabola. The vertex of the parabola is (2, 1). So, the axis of symmetry is the line x = 2.

Word problem finding the answer

  • The product of two consecutive negative integers is 1122. What are the numbers?

  • Remember that consecutive integers are one unit apart, so my numbers are n andn + 1. Multiplying to get the product, I get:

      n(n + 1) = 1122
      n2 + n = 1122
      n2 + n – 1122 = 0
      (n + 34)(n – 33) = 0 Copyright © Elizabeth Stapel 2004-2011 All Rights Reserved

    The solutions are n = –34 and n = 33. I need a negative value, so I'll ignore "n = 33" and
    take n = –34. Then the other number is n + 1 = (–34) + 1 = –33.

      The two numbers are –33 and –34.

Note that the second value could have been gotten by changing the sign on the extraneous solution. Warning: Many students get in the very bad habit of arbitrarily changing signs to get the answers they need, but this does not always work, and will very likely get them in trouble later on. Take the extra half a second to find the right answer the right way.

Word promblems

Quadratic Functions Word Problems

Cool things to know

Math in words

  • There was a negative Boy, who was confused about whether or not he should go to a radical party. The Boy was square, so he missed out on 4 Awesome Chicks and he cried until the party was over at 2 Am.

Hint: x=[-b +/- sqrt(b^2-4ac)]/2a

Q: What is the hidden math term? BOLA BOLA

A: Parabolas (pair of bolas)

Q: Why do you rarely find mathematicians spending time at the beach?

A : Because they have sine and cosine to get a tan and don't need the sun!