2. Problem
An artist is building a sculpture and is using graph
paper to graph the sculpture. The monument
consists of an arch and a straight line. The
equations of the arch and the line are below. Find
the intersections of the arch and line.
3. Step 1: Isolate y
Since y is already isolated in both equations we
can move onto Step 2.
4. Step 2: Set the equations equal to each other
Since both equations are equal to y we can set
them equal to each other like this:
5. Step 3: Get all terms to one side
Move all the terms to one side by using inverse
operations like this:
6. Step 4: Factor out the perfect square trinomial
You can use either the box method, completing
the square, or the quadratic formula. For this
example, I am going to use the box method.
7. Step 4: (cont’d)
a = 1
b = -4
c = -12
ac = -12 b = -4
2 * -6 = -12 2 + (-6) = -4
11. Try this!
A meteorite was falling from the sky and an air
balloon with a camera was traveling to try to take
pictures of it. Their trajectories are modeled by the
following equations. Where do their trajectories
intersect?