Question

4. Describe the following graph completely

a. Where is the vertex of the parabola?
b. Is there a line of symmetry? If so, draw it in.
c. Are there any x-intercepts? If so, name them. d. Are there any y-intercepts? If so, name them. ​

Answer 1

• a. The vertex is at (2,1) which is the highest point of the parabola. This applies to any parabola where it forms a hill like this.
• b. The line of symmetry is x = 2. It is the vertical line through the vertex. The line of symmetry cuts the parabola into two equal halves (one half mirrors over the line to get the other half).
• c. The x intercepts are x = 1 and x = 3, which is where the parabola crosses the x axis. More specifically the locations are (1,0) and (3,0).
• d. The y intercept is where the graph crosses the vertical y axis. The y intercept is -3, so its location is (0,-3). A function can only have one y intercept.