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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: $ ( 1, -2 ) $; point: $ ( -1, 14 ) $
Polynomial and Rational Functions
Quadratic Functions and Models
Oregon State University
In mathematics, the absolu…
In Exercises 47-56, write …
In Exercises $49-52$ , wri…
let's write the standard form for the equation of a problem. So recall that the standard form is given by the following where the Vertex is given by H K and our problem there telling us that the Vertex is one comma minus two. So that means H is one. Kay is minus two and we could plug these values in for Huk and this formula here. So update our equation so this now will become and we still need to find the value of a and the way we'LL do that is to use the fact that you're grab passes through this point. So what this means in terms of F is that when X is minus one, the Y values fourteen. On the other hand, we have a formula over here for F, So let's plug in minus one and see what happens. So plugging in minus one for X. So we have a negative two squared minus two. So that will become for a minus two, on the other hand, were given that this value also has two equal fourteen Oops. So, using that given information here, this justifies why I'm writing. This equals fourteen here and So now we have this equation for a minus. Two is fourteen. It's going and solve this for a add the two to both sides and then divide by four on both sides. And I don't give us a equals four. This was the last step because all we needed to find over here was a now we just found it before. So plug this in back to F four times and parentheses, X minus one quantity square. And then we subtract two. And this will be the standard form of the problem that has the Vertex one minus two. And it also passes through the point negative one fourteen. So that's our final answer.
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