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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.$$y=2 x^{2}+5 x+9$$

(b) None (c) None

Algebra

Chapter 1

Functions and their Applications

Section 4

Quadratic Functions - Parabolas

Functions

Missouri State University

Campbell University

Idaho State University

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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Okay, so we need to graph this y equals two x squared plus five x plus night Mhm. Maybe the first thing that shouts out at you is that that y intercept is up to nine. And we know that because that's the C value to plug in zero for X, you'll get nine for Why? Um And then the next thing I would do is figure out where the axis of symmetry is, Which is the equation? Negative B over two A. So looking at the B value is five so negative 5/2 times two because I see a value. So we're looking at negative five force. You should be pretty good at having math if you're in this class, so that's a little bit to the left of negative one. So now what you might do is using crafting calculator, too. Actually figure out what the Y value is. I say that because these are not using them. So that's what I'm going straight to the calculator and I'm typing in two times 54 squared, plus five times five force negative. I shouldn't say, uh, plus nine. And when I do that, I get the approximate decimal. 5875 That's what my calculator gave me. So 12345 like right here. So because it's the access of cemetery, it's reflected on the other side. And the whole premise here is that this parabola here's your answer. Letter A never crosses the X axis, so your answer to Part B is that there are no X intercepts. Well, you can confirm that that's true by using the quadratic formula and that says X equals negative B plus or minus the square root of B squared 25. That's about squared minus four times a times C all over to a. So, as you look closely under the radical, you have 25 minus 72. So what happens? There is We're square rooting and negative, which leaves us with a non real root. And when you have a non real root, that means we have no X intercepts. So there's your answer. The letter C as well. I'll just copy that B and C both have no X intercepts, and years later, in

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