Think of the point where the graph of an equation crosses the x-axis. This is the x-intercept. The y-value of that ( x, y) coordinate pair is 0, so to find the x-intercept of the equation, we should substitute 0 for y and solve for x.
ax^2+ bx+ c=0 ⇕ x=- b± sqrt(b^2-4 a c)/2 a
Let's identify the values of a, b, and c in our case.
0=x^2+4x-17 ⇓
1x^2+ 4x+( -17)=0
We can see that a= 1, b= 4, and c= -17. Let's substitute these values into the Quadratic Formula.
The solutions for this equation are x=-2±sqrt(21), so the x-intercepts are (-2-sqrt(21),0) and (-2+sqrt(21),0).
Finding the y-intercept
Let's use the same concept to find the y-intercept. Consider the point where the graph of the equation crosses the y-axis. The x-value of the ( x, y) coordinate pair at the y-intercept is 0. Therefore, substituting 0 for x will give us the y-intercept.
