All about standard form

by: awail deria

Learning goals:

1. maxima

2. minima

3. quadratic formula

4. completing the squares

Summary of the unit:

in the last unit of quadratics our class learned about standard form. the first thing we learned was completing the square. the way we figured this out was by changing a standard form equation to a vertex form equation by changing the first two terms of a quadratic relation into a perfect square while maintaining the balance of the original relation. when you complete the square you can answer max and min questions as we get the k value. the next thing we learned was a short lesson on how to find the r, s, vertex, AOS and graphs in the quadratic formula. quadratic formula is used in algebra to solve quadratics equations. general form is; when a, b, c, are constants in the equation. we use this formula when an equation is in standard form because variables correspond in the standard form and in the formula. another thing we were taught was the discriminant which determines how many solutions there will be. the expression in the square root is called the discriminant. if the discriminant is above 0 theres 2 possible solutions, if its below 0 there are no possible solutions, and if it equals zero theres one possible solution. the quadratic formula and completing the squares is used to help answer word problems and graph equations. when solving word problems you need a vertex. to find the x intercepts we use the quadratic formula and then find the AOS b adding two x intercepts and dividing them by two. after that we can then sub it in to find y. and thats how to get your vertex. the other way is by completing the square and changing the equation to the vertex form where the vertex is the h and k values. by having the two x intercepts and the vertex we can graph the equation or solve the word problem. in conclusion this unit was very easy for me and i learned a lot from it.

Quadratic formula example/ completing the square example

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word problem

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reflection:

the quadratics unit was long and difficult however by the end of it i learned many techniques and steps to help me solve equations and word problems using different forms: standard, vertex, and factored form. in the first unit of quadratics which was vertex form, i found it the most difficult. i thought the lessons were too complicated for me to understand over a short period of time. these lessons included the introduction to parabolas, quadratic functions, how to write equations in vertex form given the transformations, and mapping notations. i now have a clear understanding of this unit after we had the test because i understood all the mistakes i made. one of my main struggles was finding x intercepts. i didnt get why there was a negative and a positive sign in front of the square root symbol. as the three units went on i grew to understand the concept of it. the second unit of quadratics was simple, but there was many rules and steps to be followed that sometimes could get confusing on when to use which method and how. it was easy to get two different types of equations mixed up. the last unit of quadratics was the easiest to me. i didnt have any difficulties throughout it at all. the last unit was a great way to end off quadratics, it put everything together so that it all made sense. the beginning of this unit was tough but as the months went by more pieces were put together and it was much easier for me.
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