In Exercises 97–98, write the equation of each parabola in vertex...

Question

In Exercises 97–98, write the equation of each parabola in vertex form. Vertex: (-3,-1) The graph passes through the point (-2,-3).

Accepted Answer

Hey everyone here we are asked to find the equation of a parabola in vertex form which passes through the 0.5 11 and has a vertex of eight negative seven. Now the first thing we have to do is just recall the vertex form of a parabola which is F. Of X. Is equal to a times the quantity of x minus H squared plus K. And now from here we just need to note that our given vertex is the point H. K. And the given point which the parabola passes through is just X. Y. And now from here we see that we have H. And we have K. But in order to write the equation of a parabola we need to find a. So to do this we just need to plug in our given information and solve for a. So starting with ffx which is just equal to Y. So we can plug in this 11. So we have 11 is equal to a times the quantity of X which is five minus H, which is eight squared plus K which is negative seven. And now from here we can just start simplifying and solving for a. So simplifying, we have 11 is equal to a times the quantity of five minus eight which is negative three squared minus seven. And now from here we can just square this negative three. So we have 11 is equal to nine a minus seven and now getting a alone, we can first add seven to both sides giving us nine A is equal to 18. And now getting rid of this coefficient will divide both sides by nine. Giving us a. Is equal to two. And so now we have A. H and K. So we can just plug this into our formula to write the equation of the parabola. So we have F. Of X is equal to A, which we found to be two times the quantity of X minus H, which is eight squared plus K, which is negative seven. And so just rewriting quickly, we have a final answer of F. Of X is equal to two times the quantity of X minus H squared minus seven. And this is our answer here for choice D. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

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In Exercises 97–98, write the equation of each parabola in vertex form. Vertex: (-3,-1) The graph passes through the point (-2,-3).

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