# Grade 10 Quadratics

### BY: KARANBIR SINGH

## PARABOLA

The line that is made on a graph when you are graphing a quadratic equation is called a parabola. A parabola can open up or down A parabola is made up of many different points. The first point is the y-intercept. The y-intercept is the point where the parabola has contact with the y-axis. The second point is the x-intercept. The x-intercept is where the parabola has contact with the x-axis. The third point is the axis of symmetry. The axis of symmetry is the mid point of the parabola. The fourth point is the vertex. The vertex is where the parabola and axis of symmetry meet. The fifth and final point is the optimal value. The optimal value is the y value of the vertex.

## PARAMETERS

Parameters are variables that make up factor, vertex and standard equations. The variables are A,H and K. A represents the vertical stretch of the parabola. If the number is a negative number the parabola will open down wards and if the number is positive then the parabola will open up wards. The K represents how many units the parabola will go down or up. And the H represents how many units the parabola will go left or right. it the number is negative the parabola will go right and if the number is positive it will move to the left.

## SECOND DIFFERENCE IN TABLE OF VALUES

A table of values can easily tell if and equation is a quadratic relation or if its a linear relation. If in a table of values the second difference is the same it is quadratic relation. and if the first difference if the some the equation is a linear relation.

## FACTORED FORM

## Factor Form To Standard For: EXPANDING

Expanding is when you have a factored form equation and you convert it into standard form.

**(x+5)(x+7)**is in factor from and if you were to convert it into standard from it will turn into**x²+12x+35.**## COMMON FACTORING

Common factoring is used when there is a number or variable that you can divide a number evenly. For example 2x²-x. there is no common number but there is a common variable which is X so the equation would turn into x(2x-1). Another example is 3x+6. there is a common number that can divide both numbers. The number is 3. So the equation would be 3(x+2). it would be x because a number that multiplies 3 to get 3 is 1 and there is an X there so you would just put a X. there is a 2 because the number that multiplies 3 to get 6 is 2.

## FACTORING SIMPLE TRINOMIALS

Factoring Trinomials - MathHelp.com - Algebra Help

## FACTORING COMPLEX TRINOMIALS

Factoring Complex Trinomials.mp4

## DIFFERENCE OF SQUARES AND PERFECT SQUARES

Factoring Challenging expressions difference of squares perfect square trinomial

## GRAPHING FACTORED FORM

## VERTEX FORM

## HOW TO SOLVE EQUATION WHEN X INTERCEPT AND VERTEX IS GIVEN

## ISOLATING FOR X

## HOW TO GRAPH A BASIC PARABOLA

IMG 1503

## HOW TO GRAPH A PARABOLA WHEN THE H AND K ARE GIVEN

IMG 1511

## HOW TO GRAPH EQUATION WHEN A,K AND H ARE GIVEN

## STANDARD FORM

## QUADRATIC FORMULA

## GRAPHING STANDARD FORM

## COMPLETING THE SQUARE

## WORD PROBLEMS

## OPTIMIZING WORD PROBLEMS

Solving Optimization Problems using Derivatives

## DISCRIMINANT

The discriminant is in the quadratic formula. It is

**b**squared**-4(a)(c)**.If this value is a negative number there are no x intercepts in the parabola. If the value is 0 then there is one x-intersect. and if the answer is a positive number then the parabola has 2 x intercepts## RELATIONSHIP

The relationship between the 3 types of equations is that they can all be graphed.

## REFLECTION

The quadratics unit was quite difficult for me. I found quadratics on and 3 to be quite easy but I had a lot of trouble with quadratics 2. The quadratics unit wasn't my best unit. I think this because there were many parts to this unit and I think that was what confused me the most. Another thing was that I would forget which type of equations was which so I would make a lot of mistakes.