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# What is the equation of the quadratic graph with a focus of (4, 3) and a directix of y = 13? f(x) = −one twentieth (x − 4)2 + 10 f(x) = −one twentieth (x − 4)2 + 8 f(x) = one twentieth (x − 4)2 + 10 f(x) = one twentieth (x + 4)2 + 8

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Carlton Burgess on May 8, 2018

Given that the approach of the quadratic graph is (4, 3) and directrix y = 13.This means that the directrix is a horizontal line, which means that the parabola that describes the graph quadratic it should be regular of the parabola, where the x part is squared.Recall that the equation of a parabola is given by where (h, k) is the vertex of the parabola and p is the distance between the vertex and the focus or directrix. The value of p is positive if the parabola is upward and negative if the parabola is facing down.The distance between the focus and the the guideline is given by 13 - 3 = 10 and the distance from the vertex is half the distance of the guideline, therefore, the distance between the focus and the vertex is 5. Since the focus is below the directrix (that is to say, the value and the approach is 3 while the value of and guideline 13), the parable that describes the quadratic graph facing down and the value of p is negative.Therefore, p = -5the vertex of the parabola is the midpoint of the vertical of the line connecting the focus and directrix.Therefore the vertex of the parabola is the midpoint of the line joining the points (4, 3) and (4, 13) and is given byThus, the equation of the graph is given byTherefore, the equation of the quadratic graph with a focus of (4, 3) and a directix of y = 13 is