This activity is intended to supplement Algebra I, Chapter 10, Lesson 7.
Problem 1 – Match the Graph, Part 1
- In vertex form or in standard form, what happens when 0<a<1?
- If a>1, the graph will be narrow and open up. If a<−1, the graph will be what?
- What is the vertex of the parabola?
- What was your value of a for the parabola?
- What is the equation of the parabola you fit to the data?
Problem 2 – Match the Graph, Part 2
- To make the parabola open down, what must be true about the value of a?
- To make the parabola wide, what must be true about the value of a?
- What is the equation of your parabola that fits the data?
Problem 3 – Match the Double Arches
Next, match the second half of double arches.
- What do you notice about the two parabolas that formed the double arches?
- The vertex of the left arch is (−2,5.5). What is the vertex of the right arch?
- What is the equation of your parabola that matches the data?
Problem 4 – The Main Cables of a Suspension Bridge
Here is a picture of a suspension bridge. Several loops of cable are represented. See the graph below to match an equation to a particular part of the graph.
- What is the equation of the piece of the graph labeled A?
- What is the equation of the piece of the graph labeled B?
Extension – The Gateway Arch in St. Louis
The Gateway Arch in St. Louis, the “Gateway” to America, is a shape that looks like a parabola to the casual observer.
- What is your equation in standard form?
- How are the two equations similar?
- How are the two equations different?
- Expand the vertex form and convert it to standard form to make a final comparison.