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,-4) The graph passes through the point (1,4).

Accepted Answer

Hey everyone here we are asked to find the equation of a parabola in vertex form which passes through the 0.16 and has a vertex of 32. And now first we just have to recall the vertex form of a parabola which is F. Of X. Is equal to the A. Times the quantity of x minus H squared plus K. And now from here we just have to note that our given vertex is the point H. K. And our given point which the parabola passes through is just X. Y. And now from here we see that we have a church and K. But we don't have a so we can't write the equation of the parabola just yet. But to find a we can just plug in our given information and then solve for a so plugging it in we have here which is just the same as why. So we can say six is equal to eight times the quantity of X which is one minus H which is three squared plus k, which is two. And so from here we can just start simplifying, so we have six is equal to a times a quantity of one minus three which is negative two squared plus two. And now just squaring this negative two, we have six is equal to four A. Plus two. And now working to get a alone we can subtract two from both sides giving us four is equal to four A. And now to get rid of the coefficient we can divide both sides by four giving us A. Is equal to one And now from here we see that we have a H and K. So we can write the equation of the parabola in vertex four. So we have F. Of X is equal to A, which is one times the quantity of X minus H, which is three squared plus K, which is two. And now just quickly rewriting, we have a final answer of F. Of X is equal to the quantity of x minus three squared plus two, which is our answer 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,-4) The graph passes through the point (1,4).