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The parabola Y? = 4x Is shifled dow units and Ielt directnx_ units , Find an equation tor the naw parabola; and iind the now vertex, IOcus andChoose the correci equ...

Question

The parabola Y? = 4x Is shifled dow units and Ielt directnx_ units , Find an equation tor the naw parabola; and iind the now vertex, IOcus andChoose the correci equation for the now parabola bolow (y+317 =4(x+5) (+51? = 4(*+ 3) (y-5}? =46 - 3) (y - 3P 46 - 51Tha nat vonox [ [5.38 (Simpbty your ansar Type ordorod polr ) Tha e nat Iocuit [ L6 384 (Simpliy Your anawror Type an ordered par:) dureclnx 6 4 = 0J (Bioli Your @nawor )

The parabola Y? = 4x Is shifled dow units and Ielt directnx_ units , Find an equation tor the naw parabola; and iind the now vertex, IOcus and Choose the correci equation for the now parabola bolow (y+317 =4(x+5) (+51? = 4(*+ 3) (y-5}? =46 - 3) (y - 3P 46 - 51 Tha nat vonox [ [5.38 (Simpbty your ansar Type ordorod polr ) Tha e nat Iocuit [ L6 384 (Simpliy Your anawror Type an ordered par:) dureclnx 6 4 = 0J (Bioli Your @nawor )



Answers

The parabola $x^{2}=-4 y$ is shifted left 1 unit and up 3 units to generate the parabola $(x+1)^{2}=-4(y-3).$
a. Find the new parabola's vertex, focus, and directrix.
b. Plot the new vertex, focus, and directrix, and sketch in the parabola.

Okay. Said to find the axis of symmetry, we can use our formula X equals minus B over to a That's gonna be 12 divided by six, which is just equal to two. If we plug to in to the equation that will give us the Y value of our Vertex booking into is gonna give us 12 minus 24 which is negative. 12 plus four is negative. Eight and then we just need a sketch. A graph I'm gonna use a scale of to It's every two dashes is one unit. There's my axis of symmetry. X equals two, the Vertex is that too negative? AIDS to get down 8 to 1, Teoh 34 by 67 away down the bottom. Okay, I know that my Y intercept is gonna be a positive four. So 1234 right at the top of my page. Um, and that we're gonna This is gonna be a stretch by a factor of three. So we're going to go up 1/1 and then up an additional two so we can get extra points there. So we had our Vertex at two. Negative eight. Karen, next point we can do it. Three negative. Fine. And that one negative time. And then the next points were across is the Y axis. Thank you very much.

We want to identify those five properties of a quadratic over on the side as well. Sketch a graph. Well, since it's already in Burt text form, we could already answer the first question. So remember his X minus H? That means h is three. And then plus que ce okay is negative, or our access of symmetry is going to be the X coordinate of Herbert Tech. So excessive now to find our Why intercept, We're gonna plug in zero. So why intercept is when? Why is equal to zero. So this is going to be above zero is equal to those Are not why when x is equal to zero. So I was going to be zero minus three squared minus or zero minus three is three square that knives, we get nine minus four or five. So are why intercept is gonna be zero by to get the X intercept. Now we're going to do is set this equal to zero. So we set that equal to zero. Uh, first thing I'm gonna do is add for on each side of this, which would give us X minus three squared is equal. For now. We can use the zero product property. I mean the square root property two square, root each side and we'd get X minus three is eager to plus or minus two. Then we can add three over, which is going to give us executed three plus or minus two. Which tells us either X is equal to five or X is equal to one. So we'd end up with 15 not 15 10 or 50 and to determine if this opens up or down. Well, our leading coefficient A is gonna be one. An A is harder than zero. So this should open upward now to graph this. Let's go ahead and plot everything. So we have three negative four for protects, not just say like this is three of the negative pores like right here that's over text. Or why intercept is at 05 spot to say five is around here. So and then our intercepts were going to be one and five. Take those down and then we just need to conduct. So look, something kind of like this here or our sketch of the ground

For this problem we have, ah, another equation off a horizontal parabola and that these x equals Why minor three squared minus five, and we have toe graph it using the Vertex and the intercept. As we see on the right, the Vertex will be given by hnk. Age appears to be negative. Five and K appears to be three. So the Vertex will bay negative 53 so that on the graph would be located about here. Next, we'll work on the intercept. That's work on the X intercept. So the X intercept is the point where y equals zero so were calculated by making, like 10 So have zero minor three squared, minus five. There will be nine minus five equals four. So the point will be, um 40 which will bay on the XX is four units to the right. And for the why intercepts, we need to make X equals e riser for why so have zero equals. Why minor three squared minus five, which becomes why Mina three squared equals five. So we square root. So why minus three is the square root of five and there will make why three plus squared off five or why minor three is negative skirt of five. So why were B three minus skirt to five? So for the graph, we can approximate the two values. So we remembered the point will be zero, and the could calculate the three plus squared off. Three passport of five to be about were round to the nearest 10th 5.2 and the the other intercept. We're be zero and three minus skirt of five. That will be 0.8. So we'll put them approximately on the graph at 0.8. Almost had one and zero and five point. And that gives us, um, grab a lot opening to the right off course as a bigger than zero, crafting crossing the Vertex and intercepts that is the solution.

We have a number 20. It the question off a whole gentle parable is given as X equal toe I minus three whole square minus four in which we need to find the Vertex. And in the substance kept escapes the graph. So if you compare this with the standard equation for gentle parabola X equal to a why am I in SK? Hold square Bless at we will be getting e as one. We should get it and zero So parabola will be like this That is opening right words and we have where takes at. Come on, Kay, that is minus four comma three. So this is the Vertex for intercepts for Why intercept? We will plug in X equal to zero, so zero will be called toe. Why? Ministry hold square minus four. So why minus three? Holds critical to four. Which means why ministry Quito bless minors under for which is blessed minus two. So why will be equal to three plus minus two? So there will be two village of why one is three plus two. One is three minus two that he wanted fire on his one. So x intercept. Why intercepts there zero comma five and zero comma one. These two are Why? Intercepts for X intercept. We should be plugging in X intercept. Really? Plug in. Why? Court was zero X equal to zero minus three Whole square minus four nine minus 40. Call to five. So we have our X intercept says five comma. So they see the X intercept. Now we will try toe draw the graph. Yeah. Okay, so we have overtakes minus four Comma tree five. Ok, it will do. This is picks. This is where this is zero. So our vertex is first of all Vertex minus four comma tree. So if this is minus four and this is three so far, text will be here minus four. Commentary ex intercepted five comma zero So X intercept will be five comma zero. And why? Intercepts are? Why intercepts? Oh, dear. Oh, come on! And little woman Five. So this is zero comma one and the look on my five. If this is five, this is one. So our graph will look like but misted up the opening night Learn. Okay, Roughly Our graph will look like this Thinking


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