Part B Question
Draw a diagram of the archway modeled by the equation y = -x2 + 5x + 24. Find and label the y-intercept and the x-intercepts on the sketch. Then find and label the width of the archway at its base and the height of the archway at its highest point, assuming the base of the archway is along the x-axis

Question 2
After navigating the obstacle course, the team can create a computer simulation of another obstacle course. Jen and her friends decide they would like to include a curved pit in their obstacle course. They want to experiment with the equation and graph of y = x2 to see how adding and multiplying values to the function will affect the parabola.

Use the graphing tool to view the graph of y = x2 and explore possibilities for their curved pit in the questions that follow.

Part A
Question
The team first experiments with changing the position of the curved pit. In the computer program, the vertex begins on the origin, and the curve is modeled by the parent quadratic equation, y = x2.

Match each description with the equation that will create that pit.

Tiles
The curved pit is shifted down 2 units.
The curved pit is shifted right 2 units.
The curved pit is shifted left 2 units.
The curved pit is shifted up 2 units.
Pairs
y = x2 − 2
arrowBoth
y = x2 + 2
arrowBoth
y = (x − 2)2
arrowBoth
y = (x + 2)2
arrowBoth
Part B
Question
Next, the team wants to explore how it can change the steepness of the curved pit.

Identify how the graph of each equation compares with the graph of the parent quadratic equation, y = x2.