University:
Felician University
Course:
MATH-002 | Basic Math Skills-Algebra
Academic year:

2020
Views:

226

Pages:

4
Author:

5CelestialChronicle

Pre-Calculus 11: Unit 2 - Chapter 4 Review **1. Two numbers have a difference of 20. The sum of their squares is a minimum. Determine the numbers.** See Notes: [4.7] x - y = 20 x^2 + y^2 = Min y = x - 20 f(x) = x^2 + y^2 f(x) = x^2 + (x - 20)^2 f(x) = 2x^2 - 40x + 400 f(x) = 2(x^2 - 20x + 10^2 - 10^2) + 400 f(x) = 2(x - 10)^2 + 200 Vertex: (10, 200) The minimum value is 200. The two numbers are: 10 and -10 **2. Every week, a restaurant sells approximately 300 pizzas for $2.50 each. Through market research, the restaurant manager determines that for every $0.10 increase in price, they will sell 20 less pizzas. What is the price of a pizza that will maximize the revenue and what is the maximum revenue?** See Notes: [4.7] f(x) = (Pizzas) * (Price) f(x) = (300 - 20x) * (2.50 + 0.10x) f(x) = 750 + 30x - 50x - 2x^2 f(x) = -2x^2 - 20x + 750 f(x) = -2(x + 5)^2 + 800 Vertex: (-5, 800) The maximum Revenue is $800. The Price = 2.50 + 0.10x = 2.50 + 0.10(-5) = $2.00 3. The graph of a quadratic function passes through A(-5, 8), and the x-intercepts of the function are -2 and 9. What is the equation of the graph in general form? See Notes: [4.6] y = a(x+2)(x-9) y = 4/21(x+2)(x-9) y = 4/21(x^2 - 7x - 18) y = 4/21x^2 - 4/3x - 24/7 4. The graph of a quadratic function passes through points A(2, 5) and B(-4, -1). The axis of symmetry is x = 1. What is the equation of the graph in standard form? See Notes: [4.6] y = a(x-p)^2 + q y = a(x-1)^2 + q Point A: 5 = a(2-1)^2 + q 5 = a + q q = 5 - a Point B: -1 = a(-4-1)^2 + q -1 = 25a + q -1 = 25a + 5 - a -6 = 24a a = -1/4 q = 5 - (-1/4) q = 21/4 y = -1/4(x-1)^2 + 21/4 5. Graph the following equation y=4x224x + 30. Identify the vertex, intercepts, equation of A.O.S, domain and range See Notes: [4.5] 5 (1.775.0) (4.225.0) 5 0 10 -5 (3-6) Vertex: (3,-6) Axis of Symmetry: x = 3 Intercepts: X - Intercepts: (6+6,0) and (66,0) 2 Y-Intercept: (0,30) Domain: x ∈ R Range: y≥-6, yER