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(a) find the vertex and the axis of symmetry and (b) graph the function.$$f(x)=-x^{2}-2 x+7$$...

Question

(a) find the vertex and the axis of symmetry and (b) graph the function.$$f(x)=-x^{2}-2 x+7$$

(a) find the vertex and the axis of symmetry and (b) graph the function. $$ f(x)=-x^{2}-2 x+7 $$



Answers

(a) find the vertex and the axis of symmetry and (b) graph the function.
$$
f(x)=-x^{2}-2 x+7
$$

This question asks us for the access of cemetery and Vertex equation for this given equation. We know making first off label are AHAs. One R B is negative. Eight. Garcia's negative seven and then plug into the equation. Negative. Be divided by two tons. A giving US four plunk four back into the Why equation. Why forced four. Squared minus eight times four minus seven. Which negative. 20 three. Giving us a access of cemetery is our X coordinate, which is four and then our vertex as four comma negative 23.

Alrighty. Number 41. We're going to graft this one and they get fun with us and give us a nice infractions. Makes a little bit harder, but not a whole lot. Were story still going to get the Vertex the same way? So X was seven equals zero So X equals negative. Seven. Vertex It's naked of seven. That's why you for attacks. And then we want some points to the left and to the right. And if I go buy into jurors, I just go by in titters when hiss of nasty fractions. So I'm going to since I have three here. I want this to be when it's squared to be on multiple three, while the first multiple three squares be nine. So I'm going to put a negative four into seven. So that will be a three. And when you plug those numbers in, we're going to get a seven. I'm gonna go the other direction and go in negative 10 and that's also going to get me a seven. And then I'm going to go down three from that and get the negatives one and that will give me a 25 and then I will go the other direction and get a negative 13. And that will give me a 25 cm. Plug those numbers into your calculator and graphical. I've got negative. 7112345671 And I've got negative. 41234123 67 I mean, I've got negative. 10 71234567 And we're gonna have a nice little proble. It was up like that. We do have access. A symmetry go down the middle, which is X equals negative seven.

Given the function f of X equals X squared plus four X plus five. We need to find the Vertex and the axis of symmetry and do this. We need to be in Vertex form. I want to do that. We need to complete the squares. Let's change the f of x zero. It's attract five that we were isolating our variables. I'm gonna leave a spot to complete the square. So x plus what squared To complete the square. Here we would take half of the four, which is to that will be in our perfect square binomial and then square that number two squared is former and that's what we're gonna use to complete the square. You know, we need to stay balance of the sea creatures We did it. Add for to you left hand side of the equation as well. So four plus a negative five is a negative one equals X plus two squared. Add the one over. We have zero equals X plus two squared plus one and change the drawbacks of Apple Jacks. And now we have rewritten this function into a vertex form. First part of the question asked us while we're in this form. What is the Vertex? The Vertex would be at negative to positive one. And the accident symmetry goes to the X coordinate is a vertical line. X equals negative too. And then for therapy were asked a graph it. So what I faxed and blue here is our, um, solution to part a RPS is to graft. So let's plot the point. Negative 21 for our vertex kind of little head myself. There negative 21 for our vertex the active senators A vertical line through that vertex. So it's vertical interacts equals negative too. And then pick another point. Um, intercept points are nice. Like the wire deceptive, you clog zero in for X, you'll get out. Five. So 05 is on going to be on this problem and you can reflect over the accident symmetry. This point is two units to the right of the accident symmetry. So we should plot a point to units to the left of it and three points of generally enough for your proble if you're just making a rough sketch. But you could add a couple more on it to be more accurate. So there is the graph of, um, X query post for exposed five

Okay, we're given the function. Other vics equals X squared, plus two eggs minus five. We need to find the Vertex is Vertex axes of symmetry and then graph the function. So let's, um first let's Turner f of X into a zero and at our five to both sides, so five equals X squared, of course, to annex. And then we're going to complete the square in the right hand side. So to this, we need to add something so that we can write the right hand side of the equation as a perfect square. By normal, we should turn or excuse me, we should take half of the two, which is one and square it once. Where does one? And that's what we're adding to complete the square known you just a balancing the equation and add this to the left side as well. And so now we've got six equals X plus one squared. We subtract six to both sides, have X plus one squared, minus six. So, um, the answer part A. But this question, the Vertex is now gonna be at negative one negative six in the axis of symmetry is gonna be the vertical lines. X equals negative one. It goes through the x coordinate of our for attacks. So, um, can Well, up, we're gonna graph this by hand. Um, let's start with plotting our Vertex at negative one negative six. We're a little bit off here, but we'll work with it so that Vertex is at negative one one of six. Our axes of symmetry would be the vertical line, and it goes through a negative one. And that access that our line of symmetry. So, for instance, I could, um, go for finding the wide intercept. If we put zero into this function, I know we would get negative five. So zero negative five is on the graph of this parabola. It's one unit to the right of the axis. So we could reflected over the axis. And there's three points. Maybe that's all that's required of you. This is also, um, quadratic with no vertical stretch. So I know if I moved to units to the right of the accidents symmetry, we would change by moving four units up, we could reflect that point, or you could plug one into the function one square one plus two times one is uh to So we have three minus five, which is going to so one negative, too, and reflected. And that's definitely enough for our graph of the problem, and you may be able to use technology in your class as well so you can hear the graphing calculator.


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