All About Quadratics!
-First and second differences
-Parabolas & graphing
2. Quadratic Form
- Vertex form
- Standard form
- Factored form
3.Solving Problems using factored form & vertex form
4. Reflection on my Assignment
5. Quadratic formula & Discriminant
What does Quadratic mean?
First Difference & Second Differences
- If the first differences are constant, the relation is linear
- If the second differences are constant, the relation is quadratic
- Finally, if none of them are constant, the relation is neither
The picture below you can see that the opposite of 2 is -2 and that gives you the vertex (-2,4). The axis of symmetry is -2 and the parabola is open downwards since "a" is negative. With this information you can tell the vertex, the "AOS", vertical translation and the direction of opening. The last part is the x-intercepts. To get the x-intercepts you have to do the step pattern. I think the step pattern is the easiest way to find the intercepts, in my opinion.
2. Standard Form
The Standard form of the quadratic equation is written as y=ax²+bx+c. The "c" value is the y-intercept. "a" value tells us the direction of opening. In standard form you want to find the x-intercepts so we use the Quadratic Formula. I will put a pic of the formula. Basically you sub everything into the Quadratic formula and find the two x-intercepts. After you find your vertex by putting the standard form equation into vertex form and from there you will find your vertex. I will put another picture of standard form to vertex. It's very simple. If you do your work, then your good to go. In the second photo you can see how he goes from standard form to vertex.
3. Factored Form
ALWAYS REMEMBER! Don't make careless mistakes!
Solving different type of Word problems
1. The path of a basketball after it is thrown in the air is given by the following equation:
h=-.25d^2+2d+1.5 where h is the height and d is the horizontal distance in metres.
a) What is the initial height of the basketball? __________
b) What is the maximum height reached by the basketball and at what horizontal
distance does this occur at?
2. A patio measures 4m by 5m. A new and improved patio is going to be made byincreasing each side by the same amount. The area of the new patio is going to be 42m2.What are the dimensions of the new patio.
The Discriminant can tell you a lot. It could tell you how many solutions you have. You could have 2, 1 or 0. It's really easy, just sub the numbers into the appropriate variables and it should be easy to solve.