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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: $ ( -2, -2 ) $; point: $ ( -1, 0 ) $

$y=2(x+2)^{2}-2$

Algebra

Chapter 2

Polynomial and Rational Functions

Section 1

Quadratic Functions and Models

Quadratic Functions

Complex Numbers

Polynomials

Rational Functions

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Let'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'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's go ahead and plug that in over here and we'll have X minus negative too. Minus two. And let'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'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'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.

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