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(a) Draw the graph of the parabola. (b) From your graph, estimate the $x$ -intercepts. (c) Check your estimate by finding the $x$ -intercepts exactly.$$y=-2 x^{2}-4 x+9$$

$$\text { (b) }-3,4,1.4(\mathrm{c}) \frac{-2 \pm \sqrt{22}}{2}$$

Algebra

Chapter 1

Functions and their Applications

Section 4

Quadratic Functions - Parabolas

Functions

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Lectures

01:43

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x^2. The output of a function f corresponding to an input x is denoted by f(x).

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(a) Draw the graph of the …

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we need to craft y equals negative two X squared minus four X plus nine. And the first thing that you might pop out at you is to see that that why intercept is the C value is up to nine. That's from that information. Otherwise, you might want to figure out the axis of symmetry, which is that equation X equals negative. B over two A. Well, and this problem will be values negative. Four. So the negative of negative force positive for over two times the value of negative to those are found from right there. So we're looking at four divided by a negative four, because that's what two times two is to get negative one. So that's your axis of symmetry. And then to figure out the why. Sorry. The Vertex it's the X value for the axis of cemetery is the X value of the Vertex. You plug it in negative one. When you square, it's positive, and so that stays negative, too. That becomes plus four negative four times 91 then plus nine. You get a value of 11, just counting up a few more. That's where your vertex is, Um, and The thing with the axis of symmetry is it reflects points on the other side. So this why intercept got reflected over. And the downside to this graph I just drew is it's very difficult to see where they cross the X axis, so you might want to use the the A graphing calculator to figure out those points. But this is a very rough estimate for my answer for part A. So I'm just going to use a graphing calculator and see that the X intercepts appear to be about negative 3.4 and 1.4. And those values should make sense because they have to be equal. Distant from the axis is cemetery. So that looks about right. All right, so, in part C, how do you actually find the X intercepts as you set the equation for the zero and you can use the quadratic formula, which says X equals negative b so positive for plus or minus the square root of B squared. Um, minus four a. C. So four times negative two times nine all over to a two times negative two. So if you do inside of the, um, parentheses here, we're looking at her, I guess I call in parentheses, but the grouping symbol we have 16 plus 72 which is 88. So we're looking at four plus or minus square root of 88. The mayor rewrite 88 is four times 22 all over negative four. And the reason why I choose that is because now I can break that down to before, plus or minus two, Route 22. And then I can divide every one of these by negative two to simplify it. Yeah, so if I do that, I just like to have the the denominator and be positive. That's why I would divide by negative two. So it be negative, too. It's still plus or minus those two's cancel out all over. Positive, too. Is your answer for parts seat. There you go. So there see a period be and right here was a

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