Quadratic functions have the standard form of ax^2 +bx +c where a, b, and c are known values. Changing the form to a(x+h)^2 +k is called the vertex form by completing the square. There are three steps. Step 1: Isolate the constant, c Step 2: Make the leading coefficient a =1 by dividing the first...

First, find the t-critical value for right-tailed tests. There are two steps to find it. However, before starting check to see if the population standard deviation,σ, is given or not. Check the second condition, either the sample size is more than or equal to 30 or the population is normally distributed. Step 1, identify the...

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To solve equations, there are several ways. By factoring, completing the square, the formula, or graphing, etc.- However, all methods start with setting the equation equal to zero, which is very important. I’d like to show the method by factoring in this video. There are three types of solutions, one solution which is often called double root. Two solutions...

In this video, I ‘d like to show some examples of factoring method. First, always check to see if there are common factors in any type of expressions. I showed three types of formulas in this video,difference of two squares, quadratic trinomials, and perfect square trinomials. However, we can use the cross method for all...

In summary, in order to find z-critical values, we need to find the left cumulative area to look up the z-table. For left-tailed tests, since we have the left area as the significance level for the test, we use that α to find the z critical value However, for right-tailed tests, we need to subtract...

In summary, we need to find the degree of freedom and one-tailed area to look up the t-table. Please make sure that our t-table gives only positive t-scores. Therefore, we need to switch positive t-scores to negative values for left-tailed tests and must have both positive and negative values for two-tailed tests.

Since we use the left cumulative z-table, we need to find the left-tailed area to find the negative z-critical value. First, subtract the given confidence level from one and then divide it by 2 to get the left area. Look up the table using the left area to find one of the critical values. Once...

we need to find the degree of freedom and one-tailed area to look up the t-table. Please make sure to state both positive and negative critical values since our t-table only gives positive values.

When you calculate the standard deviation,make sure to use the mean. Once you find the sum of the squared deviations, you already have the numerator value of the formula. To find the number of the observations, you just count the number of x values.