Quadratics

Standard Form

Summary of standard form.

Standard form = y = ax² + bx + c

a value tells us the direction of opening. If a value is negative parabola opens downwards and if a is positive parabola opens upwards.

Quadratic formula ( in the following picture )

Completing the square help us to find Vertex and change standard to vertex form.

Today I show you the basics of Standard form like How to convert standard to vertex form.

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Standard form

Equation

y = ax² + bx + c

What does a tells us about.

a tells you the direction of opening. If a value is negative parabola opens downwards and if a is positive parabola opens upwards.

How to find Vertex by using completing the square and; convert standard to vertex form.

Example: y = 3x² + 6x - 10

y = (3x² + 6x) - 10

y = 3(x² + 2x) - 10 { Take out 3 }

y = 3(x² + 2x +1 -1) - 10 { When you divide 2/2 and then square you get 1}

y = 3(x² +2x +1) -3 -10 {Multiply 3 by -1 you get -3 and take it out }

y = 3(x² +2x +1) - 13

y = (x + 1)² - 13 { Now this is vertex form so the vertex is ( - 13, -1)


AND YOU ALSO SEE HERE HOW WE CONVERT STANDARD FORM TO VERTEX FORM.

Quadratic formula Example to find x intecepts.

Example : 2x² - 8x -24 = 0
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Discriminant

The discriminant tells us how many solutions (x-intercepts) a parabola will have.


D=b^2-4(a)(c)

a=2

b=6

c=12

D=b^2-4(a)(c)

D=6^2 - 4(2)(12)

D=36-96

D= -60


So, If the 'D' value is less than '0', than there will be no x-intercepts.

If the 'D' value is '0' than there will be 1 x-intercept.

If the 'D' value is greater than '0', than there will be 2 x-intercepts.



Video for word problem ; how to solve by completing the square and as well as about revenue.

The following video is about revenue problem in which you will see how to find revenue by using completing the square. In this video you learn revenue = Price * Quantity , as well as you learn here how to find exact revenue.
Maximizing Revenue Word Problem (Completing the Square): Straightforward Worked Example!

Word problem about how to find Rectangle dimensions.

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Word problem about consecutive integers.

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Learning goals

1. Today I learn how to work with quadratic formula.

2. Today I also learn about completing the square.