Substitute 0 as x to get the y-intercept.
To get the intersections on the x-axis you need to factorise and then the x values that make each bracket zero is the value.
E.g.
x2 + 10x + 7 = 0
(x + 5)(x + 2) = 0
x1 = -5 , x2 = -2
So the y-intercept is 7, and the x-intercepts are at x=-5 and x=-2
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Because when your solving a quadratic equation your looking for x-intercepts which is where why equals 0 and x equals what ever the answer is.
Using the quadratic equation formula: x = -1/4 and x = 2/3
The roots of the quadratic equation are the x-intercepts of the curve.
so you can find the solution for the x-values. the x-intercepts are when the graph crosses the x-axis
The x intercepts are when y=0. Substitute the zero in for all y and then solve. Use quadratic formula and reduce. I got (-1+/- sqrt 10)3 about .72075922 and -1.387425887