At the state fair, Erin and her cousin ride the Ultra Drop roller coaster. When the ride plummets down the first hill, it dips below the loading platform. At the bottom, a camera snaps the riders picture before hurtling them back toward the sky. The equation y=x^2 - 9x + 20 models the roller coaster’s path over time. The variable y represents height (in feet) above or below the platform. At y=0, the roller coaster is even with the platform. The variable x represents the amount of time (in seconds) since the ride began.

Factor and graph the equation to better understand Erin’s ride.

Part 1: write the equation in factored form.

Part 2: find the vertex of the parabola. Hint: to find the x-value of the vertex, take the average of the x-values of the x-intercepts or use the first part of the quadratic formula (x= - b/2a).

Part 3: identify the intercepts.

A. What are the x-intercepts? Hint: use the equation from Part 1.

B. What is the y-intercept? Hint: use the equation y= x^2 - 9x + 20.

Part 4: sketch the graph of y= x^2 - 9x + 20. Identify the vertex and x- and y- intercepts on your sketch.