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

$$\text { (b) }-3.7,1.2(\mathrm{c}) \frac{-5 \pm \sqrt{97}}{4}$$

Algebra

Chapter 1

Functions and their Applications

Section 4

Quadratic Functions - Parabolas

Functions

Oregon State University

Harvey Mudd College

Baylor 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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or ask to graph. Mike was two x squared, uh, plus five X minus nine. What I might do is start this problem was identified that that y intercept is down here at negative nine. Because if you plug in zero for all those exes, you get negative nine. My next thing would be to find that access to cemetery, Which is the equation? Negative B over two A. So we're looking at negative 5/2 times two. So it's a negative five. Force our access to cemeteries somewhere over here to the left of negative woman. And I know it's an upwards u shape. So I know it's going to be down here somewhere a pretty narrow graph because a. Well, it looks something like that, and you can use a graphing calculator to get a better approximation. But this is what we're looking for for part A. Uh, and then the second part is, uh, they want you to approximate these X intercepts. So for part B, your X intercepts will be about negative, right? 3.7 and 1.2. Something like that. Uh, yeah, which is pretty clear. I guess maybe it's not that clear, but we do have a positive zero, and we will have a negative zero based off of our graph. So, in part, C actually want you to find the perfect X intercepts. And you can find those X intercepts by doing the quadratic formula, which is negative B plus or minus the square root of B squared minus four a. C all over to a so as you do, you know, four times, two times negative nine, you're gonna get negative. 72. We're looking at 25 plus 72 which is 97. If we can even simplify that at all. And, yeah, I believe that's a prime number, so there's no way to break down 97. And so this is the best answer you can get for the exact answers for your X intercepts. But if you were to type those in negative five minus Route 97 all over for you get the negative answer and 85 plus Route $97 or you get a positive answer, which confirms that we have the right craft and the right X intercepts

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