Fill in the blank(s) to correctly complete each sentence.

Question

The graph of ƒ(x) = (x + 4)² is obtained by shifting the graph of y = x² to the ___ 4 units.

Accepted Answer

Welcome back everyone. If the function h of X is equal to x minus 22 is graph compared to Y equals x2, in which direction and by how many units is the graph shifted? A says 2 units to the right, B 2 units to the left, C 2 units up, and D 2 units down. So basically we're considering H of X. Which is equal to. The given function Y equals x2, let's call it G of X. Transformed right in some way. What we notice is that the outer function is still the same. We still have the square, but we are changing the value of x. It says x minus 2 instead of X. So H of X is simply G of X minus 2. And now we want to understand that this is a horizontal shift. A vertical shift means that we're adding a number to our function. So let's say if we have Y equals X2, and if we add or subtract a number C, well this is essentially a shift up or down vertically. So we can essentially say that up and down, while those options are incorrect. We want to consider a horizontal shift to the right or to the left. Now if we have a function in the form of F of X minus A, And if A is a positive number, then we are performing a horizontal shift. To the right By a units. Otherwise, if we have an expression F of X plus a. If A is positive, we end up with a horizontal shift. To the left. By a units. In this case, our expression is G of X minus 2, right? So we have a negative sign and our A. is equal to 2, so we essentially end up with a positive A value x minus 2 gives us a horizontal shift to the right by 2 units. So essentially considering the answer choices, we're going to say that A is the correct answer, 2 units to the right. Thank you for watching.

Fill in the blank(s) to correctly complete each sentence.
The graph of ƒ(x) = (x + 4)² is obtained by shifting the graph of y = x² to the ___ 4 units.

Key Concepts

Graph Transformations

Horizontal Shifts

Quadratic Functions

Watch next