in-exercises-47-56-write-the-standard-form-of-the-equation-of-the-parabola-that-has-the-indicated--9

Question

In Exercises 47-56, write the standard form of the equation of the parabola that has the indicated vertex and whose graph passes through the given point.

Vertex: $ \left(-\frac{5}{2}, 0 \right) $; point: $ \left(-\frac{7}{2}, -\frac{16}{3} \right) $

J Hardin · Accepted Answer

recall that the standard for of a parabola is given by the following equation. And now this is a problem with Vertex H Cate. And so here we are, given the Vertex H is negative five paths K equals zero. So let&#x27;s go ahead and plug those in for Agent K and then K zero So I won&#x27;t have that if we could just find the value of A that we solved the problem. And to do that we&#x27;LL use this information over here. This tells you if you plug in negative seven half for eggs, you get negative sixteen thirds for why so using our Vertex form we&#x27;ve rewrite this equation over here. It&#x27;s this equation so that we could find a way. So this expression is negative one You square that you just get one and you end up with a equals negative sixteen over three. So finally we take our first takes form and just replaced the EVA value. So that is the standard form for our problem

J Hardin · Answer

let&#x27;s write the standard form of this equation that has the given vortex five twelve and passes through the point seven fifty. So my standard form, we&#x27;re looking for an expression that&#x27;s given on the right hand side, where the point h k is the vortex. So in our case, eight people seven Excuse me, H equals five, and Katie was twelve. That&#x27;s given by this over here. So using this information, we can rewrite our earth by replacing the ancient pain. And then now we use the fact that paragraph passes through this point over here. So this means fof seven is fifteen. So let&#x27;s use that fact by plugging in seven over here into the right hand side. So we have seven minus five. That&#x27;s two. And then that square add in the twelve and were given that this equals fifteen. So then now we just have to solve for eight. So let&#x27;s go ahead and subtract this twelve on both sides that will give you for a equals three and then this implies, eh? Three or four. And now, finally, we go back to our equation f over here, and we plug in the value of a that we just found. And we leave the agent decay as they are five and twelve. So this is the standard form of the proble, and that&#x27;s our answer.

J Hardin · Answer

let&#x27;s write this standard form of the equation of a problem. So it&#x27;s for a call. What? That means Standard form eight times. Now we have parentheses. X minus h square plus que. And this is where the Vertex is given by the point h come. Okay, We&#x27;re given in our example, that the Vertex is two three. So it&#x27;s going to plug those into our formula. Over here, we can update our F equation. So now that becomes X minus two hoops X minus two square and then plus K, which is now three. We still need to find a, and the way will do that is will use the fact that our graph passes through the point zero two. What that means is that if you plug in zero for X, you know why. Values, too. So let&#x27;s use that fact. Well, come over here and plug in X equals zero. That gives you a zero minus two square plus three. As for a plus three and then by the given information, we know that this is equal to two. So now we can solve this equation for a So that&#x27;s the track three from both sides. So two minus three is negative one and then divide both sides by four. Now we found all the values we found H and K. We just found a so upload that back into F. So now our is negative. One over four parentheses, X minus two square plus three. So this is the standard form of the proble, and that&#x27;s our final answer.

J Hardin · Answer

Let&#x27;s write the standard form of the equation of a proble that has the given vortex and passes through this given point. So let&#x27;s recall what the standard form is sometimes also called the Vertex form. And the nice thing about writing it in this form is that the verse X is given by he&#x27;s calm. Okay, so in our case, the agent care given we can see over here h is negative one fourth case three house and we&#x27;LL We&#x27;LL come back and deal with this in a few moments. So let&#x27;s just rewrite our f using the given information so far So we&#x27;LL have X minus h and then plus que unless she&#x27;s go ahead and clean that up a little bit. So once we find a, we&#x27;re finished with the problem. And so now it&#x27;s time to go ahead and use this piece of information over here. If you grab passes through this point negative to zero, that means that when you plug in negative Tumen for X, you get Y equals zero. However, we could also plug in negative to it&#x27;s our formal over here, and we could see what the value is, what we know that the value zero and then we could solve for aid. So this is what happens. And then you could combine those fractions. Negative too is equal to negative eight over to excuse me and I get paid over for and then add one over four to that. Yeah. And then you get negative seven over four and we still have to square that. So this is equal to will have forty nine over sixteen times, eh? Plus three over two equals zero. And then let&#x27;s just go ahead and solve this for a So then Now we&#x27;LL go ahead and multiply both sides by sixteen over forty nine. And then at this point, we should go ahead and cancel as much as we can. So we see a negative sign will stay here in the answer two and sixteen. I could cross those off and take out an eight and then checking whether three goes into a forty nine. That doesn&#x27;t doesn&#x27;t happen, so we&#x27;ll just go ahead and keep those and saw multiply the a In the three, there&#x27;s my twenty four still have forty nine, So that&#x27;s r a simplified. And now we do is go back to our previous equation over here and just replace a with. It&#x27;s a miracle value, and that&#x27;s our final answer.

J Hardin · Answer

Let&#x27;s write the standard form of the parabola that has the Given Vertex and passes through this point here. So recall the standard form that&#x27;s a Times X minus h squared plus K where the Vertex is given by the point h. K. So here we could see that H is negative two and K is also minus two. So let&#x27;s go ahead and plug that in over here and we&#x27;ll have X minus negative too. Minus two. And let&#x27;s just clean this up a little bit, right? That is the X Plus two. Mhm. Okay, so the last thing to do here is to find the value of a and we&#x27;ll find that by using the fact that our graph passes through the point negative one comma zero. So that means when you plug a negative one for X, your wire zero. So let&#x27;s plug in negative one over here. So this will be a one square, which is just one. So we just have a minus two. However, by this piece of information over here, we know that this should all be equal to zero. And so add the two to the other side here of this new equation and you get a equals two and then just plug in this back into a and that will lead us to our final answer.

J Hardin · Answer

recall that the standard form is given by the following where the Vertex is given by the point Oops serval that type of each comma care So in our case, this&#x27;s our age This&#x27;s rk So we&#x27;Ll just plug those in And if we could find out what for what Sorry, what there is then We&#x27;re done because we&#x27;ll have all the unknowns will be determined So how do we find a will use this piece of information here which says that if you plug in negative through for X you get a four for why So we have f of negative too. So I replaced the ex with a minus two and then note that minus two equals negative for over two So combined the minus four in the minus five together So it&#x27;s a nine up their negative nine and then you can write This is eighty one Harry over four minus three or four and then we know that this is all equal to four due to this fact over here on the left. So that&#x27;s where the force coming from and then go ahead and just solve this equation over here for a so we could multiply both sides by four. That will give her to the fractions on the left and and three over to both sides, and then divide both sides by eighty one. And there is that&#x27;s r A. So the last step here. Messages replace our F with our new A value. And there it is. This is the standard form of the problem with the given vortex and passing through the given point.

Problem

In Exercises 47-56, write the standard form of th…

Problem 55 Easy Difficulty

In Exercises 47-56, write the standard form of the equation of the parabola that has the indicated vertex and whose graph passes through the given point.

Vertex: $ \left(-\frac{5}{2}, 0 \right) $; point: $ \left(-\frac{7}{2}, -\frac{16}{3} \right) $

Answer

$y=\frac{-16}{3}\left(x+\frac{5}{2}\right)^{2}$

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$y=\frac{-16}{3}\left(x+\frac{5}{2}\right)^{2}$

Precalculus with Limits

Heather Z.

Kayleah T.

Caleb E.

Maria G.

Absolute Value - Example 1

Absolute Value - Example 2

Ron LarsonPrecalculus with Limits

Heather Z.

Kayleah T.

Caleb E.

Maria G.

Ron Larson

Precalculus with Limits