Match each function with its graph without actually entering it i...

Question

Match each function with its graph without actually entering it into a calculator. Then, after completing the exercises, check the answers with a calculator. Use the standard viewing window. ƒ(x) = (x - 4)^2 - 3

Accepted Answer

Hello, everyone. We are asked to find the graph of the quadratic function F of X equals in parentheses, X minus seven closed parentheses squared minus nine. We are given a coordinate plane to work with. First recall that since this is a quadratic function, our graph will be a parabola or a U shape. Here, we have no leading negative number. So this is a positive parabola. So this will be opening upwards. So it will be an U that opens upwards from there. I recognize that this looks very similar to vertex form. Vertex form was Y equals in parentheses X minus H squared plus K. And in that form, our vertex are the values of H and K. So our vertex is also our turning point. So this is gonna be our minimum. It's gonna be the very bottom of our U shape. So comparing vertex form to R function, we're gonna find our vertex so we can graph it. So H is the value after the minus sign in the parentheses. So seven, in this case, K is the value added to the back of the parentheses which is negative nine. So our vertex is the 0.7 negative nine. And since our X scale appears to be in ones and our Y scales in fives, we're gonna count seven over to the right and down one line and a little bit before the second line and that should be the 10.7 negative nine. Now, I do know that this is a U shape because it is a parabola. But I feel like I need a little bit more than just the vertex to be able to graph it. So I'm gonna find the X intercepts. Sometimes these are also referred to as the zeros of a function or the solutions of a function. And we find this by making Y equals zero. And then we solve for X. So we would have zero equals in parentheses, X minus seven closed parentheses squared minus nine. Solving for X, I'm gonna add nine to both sides. So we have nine equals the parentheses X minus seven squared. Recall that the opposite of a square is a square root. So we will take the square root of both sides and the square of nine will be plus or minus three. And this is gonna equal X minus seven. At this point. I'm going to split this into two equations. I will have negative three equals X minus seven and I will have positive three equals X minus seven because as a quadratic, we know we will have two X values for our solutions or our zeros. So solving the negative three equals X minus seven by adding seven to both sides. I get that X equals four. So this means we're gonna graph the 40. and for three equals X minus seven, I'm gonna add seven to both sides and X will equal 10. So we will graph the 100.10 from here. I can draw my Parabola. I will do my best to draw it as neatly as possible, but please know that I am not perfect. So we will have a U shape, it will continue upward infinitely and it will pass through our vertex. And that is where this changes in direction. So the parabola with the vertex of seven negative nine that continues upwardly into the first quartile is what our graph should look like. Have a nice day.

Match each function with its graph without actually entering it into a calculator. Then, after completing the exercises, check the answers with a calculator. Use the standard viewing window. ƒ(x) = (x - 4)^2 - 3

Key Concepts

Quadratic Functions

Vertex Form of a Quadratic

Graphing Techniques

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