Math Mayhem!!

Square Root Function Transformations

The parent function of a square root is shown below.
The transformation equation of shown below.

The Rules

The transformation equation of a square root function follows several rules.

If a is negative, there is a reflection across the x axis.

if | a | is greater than one, the graph is stretched vertically.

if | a |is between 0 and 1, the graph is compressed vertically.

if h is positive, the graph is translated h units to the right.

if h is negative, the graph is translated | h | units to the left.

if k is positive, the graph is translated k units up.

if k is negative, the graph is translated | k | units down.

Example

The equation shown on the left is a transformed square root function.

The variable values and transformations are shown in the middle.

On the right, the equation in red represents the parent function and the blue represents the transformed function.

Synthetic Division

In the above photo on the right is an expression. To begin, the divisor must be put to the left in order to signify what the dividend is being divided by. In this case, as shown in the middle image, the divisor is 3, which was found by setting x-3 equal to 0 and then solving. Next, all the coefficients of the of the dividend must be placed side by side next to the divisor (as shown above in the center image). Then, the first coefficient is brought down, which in this case, is 1. That number is then multiplied by the divisor (3 x 1 = 3). The product is brought up below the next coefficient and the two are added (2 + 3 = 5). This new number is now going to be multiplied by the divisor and the process repeats until it has been done for all coefficients. Using all of the sums at the bottom, create a new expression (x^2 + 5x + 4). This, along with your original divisor, are now factors. In this case, you can further factor the expression and your final factors are (x + 3)(x + 4)(x + 1), as shown above and to the right.

What's to Come?

Quiz 4: Tuesday, 12/8

Test 2: Thursday, 12/10

Sources

Desmos

Algebra 2 Textbook