Class Notes – Using Vertex, Factored and General Forms Lesson Goal – Date ___________________ 1) The graph at the left represents the flight of a ball being thrown in the air. a) Identify the vertex of the parabola. b) When was the ball 50 feet in the air? c) Find the height of the ball after 3.5 s. d) Substitute the vertex into the equation to write the vertex form equation of the graph. 𝑦 = −16(𝑥 − _______ )! + _______ e) Expand the vertex form of the equation to write the equation in general form. f) How high was the ball when it was released? g) What was the initial upward velocity of the ball? 2) The equation of a parabola is 𝑓 𝑥 = 𝑥 ! − 4𝑥 − 12. a) Write the equation of the axis of symmetry. b) Find the coordinates (h, k) of the vertex. d) Write the equation in Vertex Form {y = a(x – h)2 + k}. e) One of the Roots is at 𝑥 = 6, where is the second root? Write the function in Factored form. 3) A projectile is shot into the air and its height at any moment t is given by the equation below (where time, t, is measured in seconds and height, h(t), is measured in feet): ℎ 𝑡 = −16 𝑡 − 4.5 ! + 324 a) What is the maximum height that the projectile will reach? Do you need your graphing calculator to determine this? Why or why not? b) Write the function in General Form and confirm that the projectile was on the ground initially. What was the rocket’s initial velocity up?