this week in math we learnt more about parabolas and I tried relating this week to last week and show you how helpful the discriminant truly is.
here we have 3 parabolas that show the different types of discriminant, in the first one the discriminant is greater than zero and intercepts the x-axis twice meaning we have 2 roots
in the next we have the parabola touch the x-axis which means we have only 1 real root
in the last one the parabola doesn’t even touch the x-axis which means we don’t have an intercept and no roots
It’s important to know the discriminant because then you know how many roots your equation will have, for example.
if discriminant < 0 then your equation will have 0 real roots
if discriminant = 0 then your equation will have exactly 1 root
if discriminant > 0 then your equation will have 2 roots
In the equation above I show you where to find the discriminant and I’ve done a question using it, in the question I did the discriminant is less than 0 meaning that it does not have any real roots
This week in math we learned about the quadratic formula
The use of it is basically to solve any quadratic equation and the way it works is….
the coefficient in front of the X squared is A, the coefficient in front of X is B, and finally the constant at the back will be C. you simply put the numbers into the formula after and do the math until you get an answer
This week in math we learned how to solve Radical Equations
up above we have one of the more complex radical equations but fairly easy if you know the steps to take
since they are both square roots you want to square them both to get rid of the root and from there you can begin the equation by moving the like terms to be paired together but don’t forget to switch the sign around once it crosses the equals sign, if it was positive it turns to negative and if it was negative it turns to positive. From there you combine the like terms which above gave us 20x and 10 and then you isolate the X by dividing 20 from both sides and you simplify to give you X=1/2. Now don’t forget to write down the restrictions, since the solution to X is greater than 0 we will put X is greater than or equal to 0
this week in math I learned how to add and subtract radicals.
in order to add or subtract a radical the radicand and the index of the radical MUST be the same
in our equation it so happens that both our radicand which is the number 2 and our index which is also an invisible 2 are the same. if it was for a cubed root the index would have to be 3 for all of them and for the actual subtraction and addition you would just subtract and add the coefficients which in the end give us 0
this week we learned about an absolute value of a real number. What that entails is how far a number away is from the number zero and with absolute values it’s always going to be positive.
In the question I show above in the barriers of the absolute values I have 5-8 which normally would give -3 but since it is within the barriers of the absolute values that means it’s going to turn into a positive 3 giving us the answer to the equation which is 7
what I learned this week in math is how to calculate the sum of infinite geometric series.
taking a look at the equation it says the sum of infinity equals the first number of your geometric series divided into 1 minus your common ratio for the series which is the term multiplied by the common ratio to give you the next term
so for this infinite geometric series the sum of all the numbers will come so close to the number 24 that it will basically equal 24
if the common ratio in an infinite geometric series is a decimal that means the series is converging and you can actually find a sum but if it isn’t a decimal then it is diverging which means you cannot find the sum
here we have my arithmetic sequence including how to find T50 and I gave the formula for Tn and with that formula you can use it to find any term.
To the bottom right of the photo you have the series part and the sum of 50 terms.