Quadratic Functions Assignment 2023 PDF

Hemeon Chapter 3 – Modelling Relationships Linear and Quadratic Functions Part 2 3.4 Quadratic Functions and Transformations Handout 1. Refer to the graph shown. a) Write down the coordinates of the vertex. b) Write the equation in the form 𝑦 = 3(𝑥 − ℎ) + 𝑘...

Hemeon Chapter 3 – Modelling Relationships Linear and Quadratic Functions Part 2 3.4 Quadratic Functions and Transformations Handout 1. Refer to the graph shown. a) Write down the coordinates of the vertex. b) Write the equation in the form 𝑦 = 3(𝑥 − ℎ) + 𝑘 c) Write down the equation of the axis of symmetry. d) Write down the domain and range. 2. Refer to the graph shown. a) Write down the coordinates of the vertex. b) Write the equation in the form 𝑦 = −2(𝑥 − ℎ) + 𝑘 c) Write down the equation of the axis of symmetry. d) Write down the domain and range. 3. Sketch. You must label the coordinates of the vertex, all intercepts and other important points you may have used. a) 𝑦 = −(𝑥 − 3) + 9 b) 𝑓(𝑥) = (𝑥 + 4) + 1 c) 𝑦 = −3(𝑥 − 1) + 12 d) 𝑓 = (𝑥 − 2) − 2 4. Write down the coordinates of the vertex. Answers: a) 𝑓(𝑥) = −𝑥 − 1 1a) (4,1) 1b) 𝑦 = 3(𝑥 − 4) + 11c) 𝑥 = 4 1d) D: {𝑥: 𝑥 ∈ ℛ}, R: {𝑦: 𝑦 ≥ 1} b) 𝑦 = 5(𝑥 − 11) 2a) (0,0) 2b) 𝑓(𝑥) = −2𝑥 2c) 𝑥 = 0 2d) D: {𝑥: 𝑥 ∈ ℛ}, R: {𝑦: 𝑦 ≤ 0} 3a) 3b) 3c) 3d) 4a) (0, −1) 4b) (11,0) 1 Hemeon 2 Hemeon 3 Hemeon 4 Hemeon 5 Hemeon 6 Hemeon 7 Hemeon 3.8 Applications of Quadratics Assignment 1. The height, ℎ, of a golf ball above ground (in meters) after 𝑡 seconds is given by the function ℎ(𝑥) = 30𝑡 − 5𝑡. a) When does the ball hit the ground? b) Find the height of the ball after 1 second. c) Find the maximum height of the ball and when that occurs. d) When will the ball be 40 𝑚 high? 2. A stone is tossed with an initial velocity of 30 𝑚/𝑠 from a height of 10 𝑚 above the surface of the moon. It's path is given by the function ℎ = −𝑡 + 30𝑡 + 10. a) What was the initial height of the stone? b) What was the maximum height reached by the stone and when did this happen? 3. Cory got a summer job assembling components to build computers. At the start of his first day, his assembly rate was low since he was just learning. As the day progressed, he was able to increase his rate of assembly, but then tired later in the day. The graph shows his rate of assembly in units per hour versus the number of hours he worked. Use the graph (no calculations are necessary) to determine: a) What was his maximum assembly rate? b) When did Cory reach his maximum rate? c) What was his assembly rate after 0.5 hours? d) When did Cory first reach an assembly rate of 6 computers per hour? 4. A football is kicked. This situation is modeled by the function, ℎ = −0.02222(𝑥 − 30) + 20 where 𝑥 is the horizontal distance the ball travels and ℎ represents the height of the ball. Assuming this is a Canadian football field of length 110 yards, calculate the height of the ball when it is kicked from the 45 yard line and crosses the opposing team's 10 yard line. Answers: 1a) after 6 seconds 1b) 25 m 1c) maximum height: 45m after 3 seconds 1d) after 2 seconds (on the way up) and after 4 seconds (on the way down) 2a) 10 m 2b) 235 m after 15 seconds 3a) 8 computers/hour 3b) after 4 hours of working 3c) 2 computers/hour 3d) after 2 hours of working 4) 6.11 yards 8 Hemeon Review 9 Hemeon 10 Hemeon 11 Hemeon 12 Hemeon 13 Hemeon 14 Hemeon 15