Period 4 - MCF3Ml-02 Functions \& Applications, Grade 11 University/College Preparation Teacher: Ms. Kaur NAME: Ryon Abu Jamaus CMIHY CARR SECONDARY SCHOOL Culminating Assignment JUNE 2023 MATTHEMATICS This assignment is worth $15 \%$ of your final mark. Check that you have all 3 pages of this exam. Answer all questions in the space provided. Calculators are permitted but are not to be shared. Put your calculator in DEGREE mode. Neat and complete solutions are required for full marks. GOOD LUCK! PART A: MULTIPLE CHOICE [6 Marks] 1. Which relation is not a function? (a.) $\{(1,1),(1,2),(1,3),(1,4),(1,5)\}$ b. $y=3 x-9$ c. $y=3-x^{2}$ d. $y=2 x-2$ 2. Finite differences can be used to classify functions. A function is quadratic if the... a. First differences are constant (b.) Second differences are constant c. First differences and second differences are constant d. Finite differences equal to zero 3. Which of the following statements about the quadratic function, $f(x)=2(x-5)^{2}-8$, is true? a. The parabola opens down b. The vertex is at $(-5,8)$ c. The axis of symmetry is at $x=5$ d. The $y$-intercept is at $y=-8$ 4. Which of the following equations is written in factored form? a. $f(x)=-x(x+3)$ b. $y=1 / 2(x-2)^{2}+3$ c. $f(x)=-5 x^{2}+10 x$ d. $y=x^{2}-16$ 5. How many real roots does the equation, $y=-4 x^{2}-8 x-4$, have? a. 1 b. 2 c. 0 d. 3 6. What are the roots of the equation $3 x^{2}-9 x-11=0$ ? a. -3.9 and 0.9 b. 3.9 and -0.9 c. $\quad 3.9$ and 0.9 d. -3.9 and -0.9 MCF3M1 Culminating Task June 2023 Page 1 of 3
Solution
Step 1 ：\(\text{1. The relation in option (a) is not a function because it has multiple outputs for the same input.}\)
Step 2 ：\(\text{2. A function is quadratic if the second differences are constant, so the answer is (b).}\)
Step 3 ：\(\text{3. The parabola opens up, the vertex is at (5,-8), the axis of symmetry is at x=5, and the y-intercept is at y=-32. So, the answer is (c).}\)
Step 4 ：\(\text{4. The equation in factored form is in option (a): } f(x)=-x(x+3)\)
Step 5 ：\(\text{5. The equation } y=-4x^2-8x-4 \text{ has a discriminant } D=(-8)^2-4(-4)(-4)=64-64=0, \text{ so it has 1 real root. The answer is (a).}\)
Step 6 ：\(\text{6. To find the roots of } 3x^2-9x-11=0, \text{ use the quadratic formula: } x=\frac{-(-9)\pm\sqrt{(-9)^2-4(3)(-11)}}{2(3)}\)
Step 7 ：\(x=\frac{9\pm\sqrt{81+132}}{6}\)
Step 8 ：\(x=\frac{9\pm\sqrt{213}}{6}\)
Step 9 ：\(x \approx -3.9, 0.9\)
Step 10 ：\(\boxed{\text{The roots are approximately } (-3.9, 0.9)}\)
