2.4 Modeling Day 2 Notes- Graphing Quadratics Objective: Write equations of quadratic functions using given characteristics. Name: Hr: Core Concept Writing Quadratic Equations Given a point and the vertex (h, A) Use vertex form: y = atx - Aj + * Given a point and a-intercepts p and q Use intercept form: y = a(x - pl(x - 9) Given three points Write and solve a system of three equations in three variables. A) The graph shows the parabolic path of a performer who is shot out of a cannon, where y is the height (in feet) and x is the horizontal distance traveled (in feet). Write an equation of the parabola. The performer lands in a net 90 feet from the cannon. What is the height of the net? Human Cannonball 40 4=a ( x- 50) + 35 (50, 35) 30 15 = a10 Height (feet) 20 10 (0, 15) 20 40 60 80X Horizontal distance ( feet) B) A meteorologist creates a parabola to predict the temperature tomorrow, where x is the number of hours after midnight and y is the temperature (in degrees Celsius). Temperature Forecast a. Write a function f that models the temperature over time. What is the coldest AY 10 (0, 9.6) temperature? (4, 0) (24. 0). Temperature (*() 9 15 -10 Hours after midnight b. What is the average rate of change in temperature over the interval in which the temperature is decreasing? increasing? Compare the average rates of change