how to find the x and y intercept in a quadratic function

Question

13+ or - the square root of 107 divided by 10

Answer 1

If x=(13±√107)/10 then the quadratic equation is:

(x-1.3+√1.07)(x-1.3-√1.07)=(x²-2.6x+1.69-1.07)=x²-2.6x+0.62=0.

This can be written 100x²-260x+62=0 or 50x²-130x+31=0.

Let's check by using the quadratic formula:

x=(130±√(16900-6200))/100=(13±√107)/10.

The x-intercepts are (13+√107)/10 and (13-√107)/10 or 1.3+√1.07 and 1.3-√1.07.

The y-intercept is 31 (by plugging x=0 into the quadratic y=50x²-130x+31).

But the y-intercept could also be 0.62 (using y=x²-2.6x+0.62). These quadratics belong to the family of quadratics:

y=a(x²-2.6x+0.62) where a is an arbitrary constant). The y-intercept is 0.62a. Since a is any constant, the y-intercept cannot be determined absolutely.