Transcript text: $c=0,-2,-4,-6 ;[-5,5]$ by $[-10,10]$
Solution
Solution Steps
Step 1: Analyzing the given information
We are given a set of graphs with different values of 'c', and the window settings are [-5,5] by [-10,10]. We are also told the values of 'c' are 0, -2, -4, and -6. The graphs are parabolas. The general form of a parabola is $y = ax^2 + bx + c$. Since the parabolas all have the same shape and only their y-intercepts are different, 'c' must represent the vertical shift.
Step 2: Matching graphs to values of c
When c = 0, the parabola passes through the origin (0,0). This corresponds to the top left graph.
When c = -2, the parabola is shifted down by 2 units and its vertex is at (0,-2). This corresponds to the top middle graph (red parabola).
When c = -4, the parabola is shifted down by 4 units and its vertex is at (0,-4). This corresponds to the top right graph (red parabola).
When c = -6, the parabola is shifted down by 6 units and its vertex is at (0,-6). This corresponds to the bottom graph (red parabola).
Final Answer:
The correct matches are: top left graph (c=0), top middle graph (c=-2), top right graph (c=-4), and bottom graph (c=-6).