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Problem 48 Medium Difficulty

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: $ ( 4, -1 ) $; point: $ ( 2, 3 ) $

Answer

$y=(x-4)^{2}-1$

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Video Transcript

Okay, so we are discussing quadratic functions, and we need to write the standard form of the equation of parabola that has the Vertex for negative one and passes through the 0.23 Okay, so let's use a graph to help us for a second. So we're told that the Vertex, which is h comma K, is four negative one. Okay, so right now the formula is y equals a times X minus h squared, plus K. So we know everything, except we don't know a yet, so we'll come back to this graph in a minute. All right, So we have Why is equal toe a X minus? H squared plus K and with the Vertex were given we have wise equal to a X minus or X plus four. Excuse me. No, Sorry. X minus four squared in the minus one. Okay, so now we need to find what a is. So we're given the 0.2 comma three. So why is three and X is too? So we have three is equal to a tu minus four is negative. Two negative. Two squared is four. Oh, this is a minus one. Okay, So, adding one to this side is for is equal to four A. Therefore, A is equal to one. So our formula is X minus four squared minus one and and we can see from our graph that the 0.2 comma three is on the graph.