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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}, -\frac{3}{4} \right) $; point: $ ( -2, 4 ) $

$y=\frac{19}{81}\left(x-\frac{5}{2}\right)^{2}-\frac{3}{4}$

Algebra

Chapter 2

Polynomial and Rational Functions

Section 1

Quadratic Functions and Models

Quadratic Functions

Complex Numbers

Polynomials

Rational Functions

Campbell University

McMaster University

Lectures

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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's our age This's rk So we'Ll just plug those in And if we could find out what for what Sorry, what there is then We're done because we'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'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'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'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.

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