Final answer:
To find the coordinates of the points of intersection between the parabola y = x² - ax and the line y = bx - ab, set the two equations equal to each other, solve for x using the quadratic formula, and substitute the x-values back into either equation to find the y-values.
Step-by-step explanation:
To find the coordinates of the points of intersection between the parabola y = x² - ax and the line y = bx - ab, we need to set the two equations equal to each other and solve for x.
Substituting y = x² - ax into y = bx - ab gives us x² - ax = bx - ab.
After rearranging the terms, we have a quadratic equation of the form ax² + (a-b)x - ab = 0. We can solve this equation using the quadratic formula to find the x-coordinates of the intersection points.
Once we have the x-coordinates, we can substitute them back into either equation to find the corresponding y-coordinates.