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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.$$y=-4 x^{2}-5 x-12$$

(b) None (c) None

Algebra

Chapter 1

Functions and their Applications

Section 4

Quadratic Functions - Parabolas

Functions

Campbell University

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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All right, We need to graph negative four x squared, Uh, minus five X minus 12. And the first thing I noticed is that seeing value his, uh, going to be down 12. Because if you plugged in zero for X, you're going to get a y value negative. 12 0 minus zero minus 12 is negative. 12. Um, So then the next thing I would do is figure out the axis of cemetery, which is that equation Negative B over two A. Well, b is negative. Five. The negative of negative five is pulsing 5/2 times. Negative four. So looking at negative, because two types of force and elevate. So if this is actually the native one, my access to symmetry is a little bit beyond halfway between zero and one. Uh, so without finding the Vertex, I don't think I need to find the Vertex to explain this. You could plug in negative 5/8 until all these, but you need to calculate her anyway. The fact that we are opening downwards and this is where my Vertex is going to be located. I know that it's going to be because it's less than one from that access that y intercept. It's going to be less than four away from that negative 12. Hopefully, that makes sense. Um, so my parabola for letter a looks, something like this, and the whole point that I'm trying to get at is where is the X intercepts? There's no way that this graph is going to cross the taxes, so feel free to use and graphing calculator to get a better Vertex. Um, but this is what we really care about. There's no X intercepts, and you can confirm there's no X intercepts by doing the quadratic formula that is X equals negative B. So five plus or minus the square root of B squared minus four A. C all over to a and I'll stop right there because what's under the radical you get 25 minus, uh, what's 16 times 12 very, very negative number? It's definitely going to be negative. Put it that way, and when you try to square it and negative, you get non real solutions, which means that we get no X intercepts so we can confirm. For part C. There is no X intercepts, C B and then a

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