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 graph the quadratic function F of X equals open parentheses, X plus seven, closed parentheses, squared minus nine. We are given a coordinate plane to graph on looking at the function we're given, I recall that this is very much like vertex form and vertex form was Y equals a multiplied by in parentheses, X minus H closed parentheses squared plus K. And that it was called vertex form because we could find the vertex by taking the values of H and K. So I'm gonna use this method to find the vertex of this quadratic function. Each is in the parentheses with the variable X in the format. It's minus H in ours, we have plus seven. So this means that we must have had a double negative in there somewhere. And our X value for our vertex is negative seven. For K, we are adding K after the parentheses. And in our example, we are subtracting nine. So our K is gonna be negative nine. So this means our vertex, the point negative seven negative nine. So I'm gonna put that on my graph should be right about there in the third quadrant from there. I need a little bit more information before I can, you know, make my parabola here. Right now. All I have is a vertex. I do know it opens upward because it is positive. There's no negative number in front of the parentheses. But I'm gonna find the X intercepts and I recall to find X intercepts, I make Y equal to zero. So this would be like writing this function as zero equals open parentheses, X plus seven, closed parentheses squared minus nine. I'm in a. So for X, so I'm adding nine to both sides, so we have nine equals the parentheses, X plus seven, close parentheses squared, the opposite of a square is a square root. So I'm taking the square root of both sides and that will give me plus or minus three equals X plus seven. So here's where I'm gonna split this into two problems because X plus seven could equal a positive three or X plus seven could equal a negative three. So splitting it, I'm going to do X plus seven equals positive three and X plus seven equals negative three. That way I get two points that I can put on my graph. X plus seven equals positive three or subtract seven from both sides. I get X equals negative four, X plus seven equals negative three. I subtract seven from both sides and I get X equals negative 10. So this means our X intercepts are the points negative 40, a negative 10 0. So I'm gonna place those on our graph negative 40 is right here just before negative five. And on the X axis negative 10 0 also on the X axis. And that should be enough for me to graph this parabola. So we call that a para is a U shape that the vertex is the turning point. And this is generally what our graph looks like. Our vertex is in the third quadrant and the U shape opens upward into the second quadrant. Have a nice day.

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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

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