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

(b) None(c) None

Algebra

Chapter 1

Functions and their Applications

Section 4

Quadratic Functions - Parabolas

Functions

Oregon State University

Harvey Mudd College

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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Our task is to graph y equals negative two X squared plus four X minus 12. And maybe the first thing that shouts out at you is that you're y intercept. Be negative. 12. Um, pretty far down here. And that makes sense to me, because if you plug in zero for X, you get a bunch of zeros and then that minus 12. And then the next thing I would do is figure out the axis of cemetery by doing negative bu for two A. Uh, so in this problem, they be value is force and negative 4/2 times negative two. So that's negative. Four divided by negative four, which is negative one. So my access a symmetry. It's just to the left of that at X equals negative one. And the other piece to recognizes your vertex goes through the axis of symmetry so I can plug in negative one and from both of these exits, Well, negative one squared is still positive. One times negative two is negative. Two. Then that minus four minus 12. Um oh, something wrong here. Negative. I by negative. Positive. That's what's wrong. So my accesses cemetery was from what happens when I try to do things too fast. You know, your axis of symmetry is over here at night. Singles one. Now that I fix that, this becomes a negative to stow. But that's plus forward and that might as well. There we go. So we're looking at negative 10. So your vertex is at one negative 10, and the nice thing about a accesses cemetery is that needs to be reflected on the other side. So what we're looking at is this downwards you down this problem for your solution apart. A supposed to surplus and greens are about all these different colors, but it definitely does not cross the X axis. So there are no X intercepts, and you can prove that there's no X intercepts by doing the quadratic formula. The quadratic formula says that X equals negative b so negative four plus or minus square root of B squared finest for a I give two times see a year 12 all over to a But if you look closely at the radical, what we have is 16. I'm just using a calculator 16 minus four times negative two times negative 12 gives me negative 80 If we square root a negative, get a non unreal solution. So that means that it will never cross the X axis. Um, so there's no X intercepts. That's your answer for letters. C as well. There's no X intercept, and here's your answer that end.

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