MCF3M Unit Test Quadratic Functions PDF

𝟓𝟎 MCF3M Unit Test 𝟓𝟎 Quadratic Functions Name: ____________________ 1. For each of the following relations, determine the domain and range and whether or not it is a function. [9 marks] a. for each of the...

𝟓𝟎 MCF3M Unit Test 𝟓𝟎 Quadratic Functions Name: ____________________ 1. For each of the following relations, determine the domain and range and whether or not it is a function. [9 marks] a. for each of the following Domain: ___________________________ Range: ___________________________ Function? ___________________ b. {(5,-2), (6,-5), (7,-2), (8,-1)} Domain: ___________________________ Function? ___________________ Range: ___________________________ c. Domain: ___________________________ Range: ___________________________ Function? ___________________ 2. Consider the function 𝑓(𝑥) = 2𝑥 2 − 3. Determine the following: [5 marks] a. 𝑓(−4) b. 𝑓(3𝑚) c. 2𝑓(−1) 3. Determine the degree of the following functions: [2 marks] a. 𝑓(𝑥) = 2𝑥(𝑥 + 4) b. 𝑓(𝑥) = (𝑥 − 3)(𝑥 + 2) − 𝑥 4. Complete the following chart: [16 marks] 𝟏 Equation 𝒚 = −𝟐(𝒙 + 𝟑)𝟐 + 𝟒 𝒚= (𝒙 − 𝟏)𝟐 + 𝟓 𝟐 Vertex (h,k) Number of x-intercepts Transformations from 𝒚 = 𝒙𝟐 Domain Range 5. Write an equation for the parabola that satisfies each set of conditions: [4 marks] a. vertex: (0,-2) 1 congruent in shape to 𝑦 = 3 𝑥 2 ___________________________________ 2 x-intercepts b. axis of symmetry: 𝑥 = −4 congruent in shape to 𝑦 = 5𝑥 2 ___________________________________ range: {𝑦 𝜖 𝑅 | 𝑦 ≤ 6} 6. A function is defined by the equation, 𝑓(𝑥) = 3(𝑥 + 1)2 − 8. [8 marks] a. Draw and label each transformation to the graph of 𝑦 = 𝑥 2 to get to 𝑓(𝑥). b. What is the minimum/maximum value of the transformed function, 𝑓(𝑥)? c. Label the axis of symmetry, the vertex, and 2 other points of the final graph, 𝑓(𝑥). 7. The height of the football after it’s kicked is modelled by the function ℎ(𝑡) = −5(𝑡 − 2)2 + 21, where 𝑡 is time in seconds and ℎ(𝑡) is height in metres. [6 marks] a. What is the maximum height of the football? b. At what time does the football reach its maximum height? c. What height was the football when it was kicked? d. What is the height of the football at 𝑡 = 1.5 seconds?