This graph allows you to manipulate the standard form of the quadratic equation, f(x)=a(x-h)²+k. Use the sliders to adjust a, h, and k.
The green dot is the vertex of the parabola.
The orange diamond is the y-intercept.
The red x's are the x-intercepts.
The pink dashed line is the axis of symmetry.
1. Which numbers - a, h, and / or k - influence the line of symmetry? The vertex?
2. Which numbers - a, h, and/or k - influence whether the graph opens up or down. Complete the following sentence: If ___ is positive, the graph opens ______. If ___ is negative, the graph opens ______.
3. Which numbers - a, h, and/or k - influence whether the vertex is above or below the x-axis? Complete the following statement: If ___ is positive, the vertex is ___ the x-axis. If ___ is negative, the vertex is ___ the x-axis.
4. Which numbers - a, h, and/or k - influence whether the vertex is to the right or left of the y-axis? Complete the following statement: If ___ is positive, the vertex is to the ___ of the y-axis. If ___ is negative, the vertex is to the ___ of the y-axis.
5. What other patterns do you see?