Station 1 – Graphing Quadratics For each of the following questions, find the vertex, axis of symmetry, and y-‐intercept.
Station 2 – Writing Quadratics
1. Create a quadratic function in standard form with zeros −7 and 2. 2. Create a quadratic function in vertex form with vertex (2,−4).
3. Create a quadratic function in standard form with zeros -‐2 and 0.
4. Create a quadratic function in standard form with zeros ±7𝑖.
5. Create a quadratic function in standard form with vertex (−2,−18)
and y-‐intercept (0,−10).
1. 𝑦 = −2 𝑥 − 2 ! + 5 vertex: AoS: y-‐intercept:
2. 𝑦 = −𝑥! + 4𝑥 − 3 vertex: AoS: y-‐intercept:
3. 𝑦 = −3𝑥! + 6𝑥 + 1 vertex: AoS: y-‐intercept:
4. 𝑦 = 𝑥 − 1 ! + 4 vertex: AoS: y-‐intercept:
Station 3 – Solving Quadratics Solve the following using any method of your choice. You MUST use each method one time – QF, factoring, completing the square, and square roots. 1. x2 = 6x – 11 2. 4x2 + 1200 = 0
3. p2 = 6p – 20 4. x2 = 12p + 45
Station 4 –Quadratic Applications 1. The length of a rectanglular piece of cardboard is 2 less than 3 times its
width. If the area measures 65 𝑚!, find the length of the rectangle.
2. An object is launched into the air from a ledge at an initial vertical velocity of 96 feet per second. Its height H, in feet, at t seconds is given by the equation 𝐻 = −16𝑡! + 96𝑡 + 16 .
a. Find all times t that the object is at a height of 160 𝑓𝑡.
b. What is the height of the ledge? How do you know?
3. The height in feet of a golf ball hit into the air is given by ℎ = −16𝑡! + 64𝑡, where t is the number of seconds elapsed since the ball was hit.
a. What is the maximum height of the ball? How long does it take to reach this height?
b. How long does it take for the ball to hit the ground?
c. Determine all values of 𝑡 for which the ℎ > 48.
Station 5 –Imaginary Numbers Simplify and show all work!
1. −84 + 36 2. (3𝑖)(4𝑖)(−9𝑖)
3. −3 1 + 2𝑖 + 2𝑖 3 − 4𝑖
4. 3 + 5𝑖 ! + 6 − 2𝑖 !
5. Evaluate 𝑖!".
Station 6 – Converting Quadratic Forms 1. Convert the following from standard to vertex form. a. y = x2 + 4x –7 b. y = x2 +10x +5 2. Convert the following from vertex to standard form. a. y = (x + 9)2 -‐ 3 b. y = 2(x -‐ 5)2 + 12