Quadratic Relationships

Summerzing the entire Quadratics

The topics that i have learned in Quadratic Relationships:

  • Analyzing Quadratics
  • Finding the given equation
  • Determine the equations from the graph
  • Factoring

Analyzing Quadrates

  • Make table of values for x-intercept and y-intercept.
  • If the first differences are equal, it would be considered as linear relationships.
  • If the second differences which are equal, it would be considered as quadratic relationships.
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Finding the given Equation

  • The vertex of this parabola is (-2,8). Add these two points in the vertex formula.
  • There is also a given x-intercept which is (2,0). To make an equation, Insert these two points to the same formula and make an equation by solving it..
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Determine equations from the graph

  • If the parabola open downwards, it means the "a" will be negative.
  • To find the "a" value, The parabola passes through the point (0,2). So substitute these two points in the same formula and solve it by the BEDMAS method.
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Part 2

Expanding

- we have given the equation in the factor form so we have to expand the equation and simplify it.

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Common Factoring

- In common factoring, in each equation solve it by finding the greatest common factor.
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Factoring By Grouping

- Factor by grouping, there are two equations basically.

- in this equation find two common pairs.

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Factoring Simple Trinomials

- In simple trinomials factoring, we expand the equation and it become into a standard form and then we slove it by using the algebric tiles, same that we used in expanding.

-The big two boxes are known as X square, the long two bars are the x's and the tiny little squares are the numbers and in each pair one is negative and the other one is positive.

- In this equation, Multiply 2 with everything inside the bracket.

- Add 2 tiles in the length side.

- Add 3 tiles at the width side.

- Fill all the areas.

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Factoring Complex Trinomials

- In Factoring Complex Trinomials, we do the oppsite from the simmple factoring trinomial by making the standard form of equation into a factor form.

- also, the x square has a number with it so we wanna make it sure if we are solving the equation in a proper way.

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Factoring Special Trinomials- Difference of Squares.

- In difference of squares, we multiply two numbers to find that given number and then put it in a factor form.

In complex problem, we find the GCF and then put it the factor form.

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Perfect squares

In order to find the perfect squares, we use a special formula so we could get the answer for standard form equations.
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PART 3

Completing the Squares

- In this situation we complete the square by making the standard form into the vertex form as the the example are shown below.
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Solving Quadratic Equations

solving the equation by finding the zero's.
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Solving Standard Form Equations

- Standard form equations are solved by using the formula which is called the Quadratic formula.

- we use this formula to find the x's, axis of symmetry which is our x-int and an optimal value which is known as y-int. This will be our vertex if we graph it.

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Quadratic Word Problems

- To find the solution, we solve the quadratic problem by using the Quadratic formula!


Q) A fireball is fired and follows a path modeled by y=-0.1x 2 +1.6x+5.7, where x is the horizontal distance from the start, and y is the vertical height of the ball.
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Revenue Word Problem

Q) Calculators are sold to students for 20 dollars each. 300 students are willing to buy them at that price. For every 5 dollar increase in price, there are 30 fewer students willing to buy the calculator. What selling price will produce the maximum revenue and what will the maximum revenue be?
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Area word problem

Q) The length of a rectangle is 6 inches more than its width. The area of the rectangle is 91 square inches. Find the dimensions of the rectangle.
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Consecutive word problem

Q) The product of two consecutive numbers is 5624. What are the two numbers?
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Right Triangle Word Problem

Q) One leg of a right triangle is 1 cm longer than the other leg. The length of the hypotenuse is 9 cm greater than that of the shorter leg. Find the lengths of the three sides.
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Discriminants

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