# Standard Form of a Quadratic Equation

Topic:
Parabola
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?