Final answer:
To find x-intercepts, one must set the equation equal to zero and solve for x. The vertex can be found using the formula -b/(2a) for the x-coordinate and substituting it into the equation to find the y-coordinate. The provided solutions need to be checked with these methods to ensure accuracy.
Step-by-step explanation:
The question asks about finding x-intercepts and the coordinates of the vertex for given parabolic equations. To find the x-intercepts, we must solve the equation when y=0 (i.e., set the quadratic equation to zero and solve for x). To find the vertex, we can use the formula -b/(2a) to find the x-coordinate and then plug it back into the original equation to find the y-coordinate.
For example, if we have a quadratic equation of the form ax^2 + bx + c = 0, the x-intercepts are found using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a), and the vertex's x-coordinate is found with x = -b/(2a). None of the options provided (A, B, C, D) are correct without further calculations to validate the x-intercepts and vertex coordinates.