write-an-equation-of-the-parabola-that-has-the-same-shape-as-the-graph-of-fx3-x2-or-gx-3-x2-but-wi-5

Question

Write an equation of the parabola that has the same shape as the graph of $f(x)=3 x^{2}$ or $g(x)=-3 x^{2}$ but with the given maximum or minimum.
Maximum $=4$ at $x=-2$

Ankit Gupta · Accepted Answer

we have given it pushing you the right in equation off. The parable of that has the same safe as the graph off FX is a quick little to the excess bed or G X is equal toe minus three xs breath. But with the given maximum or minimum, we have given the well maximum ease maximum is a little X for the pool at excessive. Well, don&#x27;t do so we can say a fence Our panel below has oh maximum hurt minus two and full I parabola must be similar So I&#x27;ll pal Ebola must be similar. Two effects is equal to minus three Xs where no, we need to save this value so we can diet if this if X who by minus two so recondite access it will do X minus minus two that is X Plus two. And when we&#x27;re sifting, if we sift away who by? We have something where you buy minus two but this will before here given in double vortex. So when we&#x27;re suffering this one so we can write our function as effects of the corridor minus the excess square. Bless full. Or we can simply putting the food. The violence so we can write. FX is acquittal when we&#x27;re boarding this value off eggs to exit X plus two Bless full. It will be the square, so our answer will be minus the excess quest minus 12 x minus eight.

Suman Saurav Thakur · Answer

so you have well, that number is fine in of it. We need to select the parent function from my fax equal to three X squared and G X equal to minus three X Square and the writer function with given conditions. What are the conditions? First condition is minimum. It called to zero, which occurs at X equal toe 11. So ven already sent mediums at zero. So our parabola must open upwards so that this point becomes a minimum. And combining these two points that is X coordinate and why according becomes overtakes doctor required parabola That is where text must be 11 comma zero and let us right It is at comma K that it articles too 10 and K call to zero now for this before parabola to open up a should be greater than Zito Positive so here a three. So this should be there bed and functions So bad function is F X equal to three x square Now we need to we need to the verdict for dysfunction So it&#x27;s the question must be at checks Let us say at X equal to three x minds at square bless key where sk it close to 11 and zero, respectively. So our question will be three x minus. Those that is this is 11 x squared plus zero. So at sexy cool too. Three X minus 11. Whole square should be our answered. Thank you.

Ankit Gupta · Answer

we have given a cushion, right? Any question off the parabola that is the same shape as the function? F X is equal to three Xs. Where RG excess Purdue minus three Xs squadron. But with the given maximum or minimum, we have your minimum value. Minimum is the Quito&#x27;s little at X is it will do 11. So we can say that since vortexes no or they seize 11 and zero, there must be See Melo with it. Affects is acquittal plus three Xs Where so what we need to do here We&#x27;re just sifting. If me saved away by zero on and X by 11 so we can write your accident will do X minus 11. So our question will be affects his acquittal three and the year X is X minus 11 and plus zero. So when we&#x27;re solving this one, so we&#x27;ll get around So three x squared minus 66 x plus 3 +63

Suman Saurav Thakur · Answer

they have Problem number 56 56 in which we need to select the baron function from affects equal toe three Xs square and G X equal to minus three x square according to the conditions Given whatever the conditions, conditions minimum many mom is zero and X equal to nine. So many army zero means parabola must be open upward and foot parabola toe open upward. A must be getting zero a means coefficient of export. But this should we are parent function that affects we will select affects equal do the excess square. Now our vertex will be nine common 09 common zero with just the right it is Etch McKay magical to nine and capable do on a Zito. No, Let us Apulia function at checks. Transformations off, but it more tips, Buddy X minus at a square bless case where h Comma K is the new word X. So how about a question? Will be It was in a parable will be xn minus nine whole squad Les que square That is every square there will Tex equal to three into Axl, minus nine hole square. So they should be bounce. Thank you

Ankit Gupta · Answer

we have given a question. You write an equation off the parabola that has the same shape as the graph off affects is equal to three X squared for G X is equal to minus three Xs problem, but with given maximum or minimum we have given minimum is equal to zero at X is equal to night. So weakened, right? Our work eg zeal who are takes is vortexes nine and zero. It must be we can say that ate the bus to be similar. Oh, to effects is acquittal to the excess. Glad. So when we are putting this well Or we can say that if we slive expert in it by nine so that we can write acceptable do explain us night And when we sifted, if they&#x27;re safe turd right by his little So we can write an equation with the help of this that affects is a little three and your value affects can be changed With x minus night plus lies, it&#x27;ll weaken died This this is in the form of a spread. So when we are following the situation But we can get on on. So as this can region in the formula a minus people. It&#x27;s stress, so we can solve this one and we&#x27;ll get three exist. Where minus 54. X plus 2. 43.

Suman Saurav Thakur · Answer

number 54 for number 54 in which it is given that we need to select the question from three X squared efforts will trace square or G X equal toe minus three x squared and shift the vertex For this. It is given that maximum maximum is minus seven at X equal do five. So parabola generally will look like because it isn&#x27;t maximum at minus maximum minus seven at X equal to five. So they said in maximum in minus seven at X equal to file. So it is our Vertex. Our vertex is new. Vertex bit vividly Use is five common minus seven and which is let us say at K were article 25 and they call two minus seven now since parable white opening downwards. So a must be negative. So we must choose the X equal to minus three x squared as bad function. No, If we write Aztecs equal to shifting off Ah, where takes I&#x27;m talking about did it would do minus three x square so it must be returned as in my industry X minus at square Bless key. There we will just Blufgan at equal toe file This five and cake will do. Minus seven over here. So it will be three X minus five squared. No bless. Minus seven. So that&#x27;s sick. What would it be? My industry X minus five whole square minus seven. This should be our said. Thank you.

Problem

Write an equation of the parabola that has the sa…

Problem 53 Hard Difficulty

Write an equation of the parabola that has the same shape as the graph of $f(x)=3 x^{2}$ or $g(x)=-3 x^{2}$ but with the given maximum or minimum.
Maximum $=4$ at $x=-2$

Answer

$f(x)=-3(x+2)^{2}+4$

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$f(x)=-3(x+2)^{2}+4$

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