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
- 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.
- we have given the equation in the factor form so we have to expand the equation and simplify it.
Factoring By Grouping
- in this equation find two common pairs.
Factoring Simple Trinomials
-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
- 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 complex problem, we find the GCF and then put it the factor form.
Completing the Squares
Solving Quadratic Equations
Solving Standard Form Equations
- 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.
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.