The topics that i have learned in Quadratic Relationships:

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

• 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.

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..

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.

Expanding

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

Common Factoring

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

Factoring By Grouping

- Factor by grouping, there are two equations basically.

- in this equation find two common pairs.

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.

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.

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.

Perfect squares

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

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.

solving the equation by finding the zero's.

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.

- 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.

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?

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.

Consecutive word problem

Q) The product of two consecutive numbers is 5624. What are the two numbers?

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.