Graph each function. See Examples 6–8.ƒ(x) = 2(x - 2)² - 4

Question

Accepted Answer

Hello, everyone. We are asked to draw the graph of the following function F of X equals four, multiplied by the parentheses. X minus four parentheses squared minus six. We were given a Cartesian plane where the X and Y axis have a scale of one unit. The X axis ranges from negative 15 to 15. The Y axis ranges from negative 10 to 15. So rewriting our function again, we have F of X equals four, multiplied by the parentheses, X minus four. The parentheses are squared minus six. So we need to first try to determine what is our parent function. What will this function look like if it wasn't stretched, flipped or shifted? And our parent function here would be G of X equals X squared. So the X squared function, I'm gonna just make a quick little rough sketch. The X squared function is a parabola with a vertex at 00. So it's a U shape. So now let's look at what we're given and see how does that apply to our U shape. So first, I notice that in the parentheses, I have X minus four by subtracting four from our parent function. We are now going to shift the vertex and the entire graph four units right before I mark that on the graph, I'm gonna notice the negative six at the end that we're subtracting six because by subtracting six from the entire function, we are going to shift the vertex down six units. So now I know that I need to shift my vertex right four units and down six units. So I'm gonna do that. So right, four down six gives me a vertex at the 0.46 I'm sorry, four negative sex. So from there, I need to figure out what does this other value tell me. So we haven't dealt with the four that's in front of the parentheses yet. So that value we say that this is stretched and it's stretched by a factor of four. So this means it gets more narrow instead of getting wider, we are gonna get it shrink shrunk in a little bit. So when we do so a sketch of this graph would have a U shape that's a very narrow U shape with a vertex at four negative six. And I am sorry that that is not super curved. Let me try that again. And generally our graph will stay in the 4th and 1st quadrants for this, but our vertex is at four negative six. And our parabola is a skinny Parabola have a nice day.

Graph each function. See Examples 6–8.ƒ(x) = 2(x - 2)² - 4

Key Concepts

Quadratic Functions

Vertex Form of a Quadratic

Transformations of Functions

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