### Student Page 4.5.3 Angry Birds and Quadratic Functions

The video game, Angry Birds, has become so popular that now there are toys and movies created with the popular animals defending their homes from the visiting pigs. Why do we care? Because every time you launch an angry bird, the bird takes a parabolic flight path! To find the equation for the path of an angry bird, revisit your work with Transformation of Functions. Complete the student page, Angry Birds and Quadratic Functions, to think more deeply about transforming functions.

#### 1.

The graph in Figure 4.5.3.1 shows an Angry Bird waiting to be launched to hit a pig. The bird must go from the origin \((0, 0)\text{,}\) through the point \((5, 4)\text{,}\) and hit the pig located at \((10, 0)\text{.}\)

What equation will allow the Angry Bird to take the right path? Write an equation. Show the work you do to find the equation in the space to the right of the picture.

#### 2.

Find both coordinates of the vertex of the quadratic function in Student Page Exercise 4.5.3.1 Write the vertex as an ordered pair. How do you know your solution is correct?

#### 3.

Suppose the Angry Bird is launched from \((0,2)\text{,}\) the pig is sitting on a pedestal at \((10,2)\text{,}\) and the bird's path must go through \((5, 6)\text{.}\) Adjust your equation in Student Page Exercise 4.5.3.1 for this new scenario. Explain how you know you are correct.

#### 4.

Find both coordinates of the vertex of the equation in Student Page Exercise 4.5.3.3. How do you know your solution is correct?

#### 5.

Suppose the Angry Bird was launched from \((-1,0)\text{.}\) What equation would you need to use to hit a pig at \((9, 0)\) and go through the point, \((h, 4)\text{,}\) where \(h\) is the \(x\)-coordinate of the vertex? Show your work.