Final answer:
To find the y-intercept of the equation x² +8x−20, set x to zero and solve for y, yielding a y-intercept of (0, -20). To find the x-intercepts, set y to zero and use the quadratic formula with a = 1, b = 8, and c = -20 to solve for x, resulting in two x-intercepts.
Step-by-step explanation:
To find the x and y-intercepts for the quadratic equation x² +8x−20, we set each variable to zero in turn and solve for the other.
Finding the y-intercept:
Set x to zero:
0² + 8(0) - 20 = -20. So, the y-intercept is at (0, -20).
Finding the x-intercepts:
To find the x-intercepts, set y (or the function itself) to zero and solve for x:
x² + 8x - 20 = 0. Using the quadratic formula x = (-b ± √(b² - 4ac)) / (2a), where a = 1, b = 8, and c = -20, we find two values for x that satisfy the equation. These are the x-intercepts.