Algebra-1

Question Analysis
This question tests the student's ability to solve a system of linear and quadratic equations graphically. The student needs to find the intersection points of the given parabola and line.

Key Concept Explanation
The key concept here is understanding that the solutions to the system of equations are the points where the parabola and the line intersect. The number of solutions corresponds to the number of intersection points.

Step-by-step Solution
1. Plot the parabola . The vertex can be calculated using the formula . Substituting into the equation gives the vertex coordinates .
2. Plot the straight line . The slope is -1 and the y-intercept is 2.
3. Find the intersection points by solving the system of equations. Set and simplify to get

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