Roger N. answered • 03/30/18

Tutor

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. BE in Civil Engineering . Senior Structural/Civil Engineer

Write the formula for the parabola that has x- intercepts (1.3,0) and (−1.3,0), and y- intercept (0,169)

Solution:

let me start by the following correction:

The y intercept is (0,1.69) and not (0,169)

So the intercept form of the quadratic equation is y=a(x-p)(x-q)

where (-1.3,0)=(p,0) and (1.3,0) is (q,0); then p=-1.3, and q=1.3

With the vertex being at the y axis and the intercepts at the x axis means that the parabola opens down. then 1.69=a(0+1.3)(0-1.3), 1.69=-1.69 a, a=-1

Substituting, y=-1(x+1.3)(x-1.3) note that this is difference of two squares y=-[x

^{2}-(1.3)^{2}] , y=-(x^{2}-1.69), y=-x^{2}+1.69
Roger N.

^{2}-1.3^{2}), y=-100(x^{2}-1.69)^{2}+169 is the equation of the parabola that opens down03/30/18