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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.$$y=2 x^{2}+4 x+5$$

(b) None (c) None

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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all right, We have to graft this y equals two x squared plus four X plus five and a problem like this. I would find the Vertex first and you find the Vertex by doing this equation negative B over two A. Well, the B value is negative as four. So it's negative for over the A value is to just make sure you multiply first. I always have students. I want to. I don't know what they're doing, but anyway, you have to do two times two first and then negative four divided by four is negative one. So my vertex is located at the export and one is negative one. So as I plug in negative one here and here, I end up with a positive one. So that turns out into two times one and uh minus 44 times one plus five. What's that? Negative two plus five is three. So on my graph, I know that I'm going left wine up to three. And, uh, it's opening upwards because I have a positive a value, and the C value is my y intercept. So I know it's going to cross at a Y intercept of five. Um, and this is a good graph. I'll even label the Vertex here, which I wrote out the Y intercept at 05 um, trying to think of anything else because when you get to part B, there are no X intercepts, and you can confirm that there's no X intercepts because if you set this equation equal to zero and did the quadratic formula, Um, what you would find is X equals negative B plus or minus the square root of B squared minus four a. C all over two a. Right here, you're gonna get an imaginary route which confirms that there is no X intercept for part C, yeah.

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