Mid-Chapter Quiz: Lessons 4-1 through 4-4
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1 1. Find the y-intercept, the equation of the axis of symmetry, and the x-coordinate of the vertex for f (x) = 2x 2 + 8x 3. Then graph the function by making a table of values. 2. Determine whether f (x) = 5 x 2 + 2x has a maximum or a minimum value. Then find this maximum or minimum value and state the domain and range of the function. Here, a = 2, b = 8, and c = 3. To find the y-intercept, substitute. f(x) = 2(0) 2 + 8(0) 3. f(x) = 3 y-intercept = 3 The equation of axis of symmetry is. For this function, a = 1, so the graph opens down and the function has a maximum value. The maximum value of the function is the y- coordinate of the vertex. The x-coordinate of the vertex is or 1. Find the y-coordinate of the vertex by evaluating the function for x = 1. The equation of the axis of symmetry is. Therefore, the x-coordinate of the vertex is 2. Graph the function. The domain is all real numbers. The range is all real numbers less than or equal to the maximum value, or. esolutions Manual - Powered by Cognero Page 1
2 3. MULTIPLE CHOICE For which equation is the axis of symmetry x = 5? A f (x) = x 2 5x + 3 B f (x) = x 2 10x + 7 C f (x) = x x 3 D f (x) = x 2 + 5x PHYSICAL SCIENCE From 4 feet above the ground, Maya throws a ball upward with a velocity of 18 feet per second. The height h(t) of the ball t seconds after Maya throws the ball is given by h(t) = 16t t + 4. Find the maximum height reached by the ball and the time that this height is reached. The maximum value of the function is the y- coordinate of the vertex. Test option A. The x-coordinate of the vertex is or Here, a = 1, b = 5, and c = 3. Find the y-coordinate of the vertex by evaluating the function for t = The equation of axis of symmetry is. The ball reached the maximum height of feet at seconds. So, this option is incorrect. Test option B. Here, a = 1, b = 10, and c = 7. The equation of axis of symmetry is. 5. Solve 3x 2 17x + 5 = 0 by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located. Graph the function. Therefore, option B is correct. The x-intercepts of the graph indicate that one solution is between 0 and 1, and the other solution is between 5 and 6. esolutions Manual - Powered by Cognero Page 2
3 Use a quadratic equation to find two real numbers that satisfy each situation, or show that no such numbers exist. 6. Their sum is 15, and their product is 36. Let x be a number and so the number is (15 x). 8. MULTIPLE CHOICE Using the graph of the function f (x) = x 2 + 6x 7, what are the solutions to the equation x 2 + 6x 7 = 0? F 1, 6 G 1, 6 H 1, 7 J 1, 7 Solve the quadratic equation. The x-intercepts of the graph indicate that the solutions are 7 and 1. So, the correct option is J. 9. BASEBALL A baseball is hit upward with a velocity of 40 feet per second. Ignoring the height of the baseball player, how long does it take for the ball to fall to the ground? Use the formula h(t) = v 0 t So, the two numbers are 3 and t 2 where h(t) is the height of an object in feet, v 0 is the object s initial velocity in feet per second, and t is the time in seconds. 7. Their sum is 7, and their product is 15. Let x, be the first number. Then 7 x is the other number. x(7 x) = 15; x 2 + 7x 15 = 0. Since the graph of the related function does not intersect the x- axis, this equation has no real solutions. Therefore, no such numbers exist. Substitute h(t) = 0 and v 0 = 40 in h(t) = v 0 t 16t 2. So, the ball takes 2.5 seconds to fall to the ground. esolutions Manual - Powered by Cognero Page 3
4 Solve each equation by factoring Write a quadratic equation in standard form with roots 6 and Write the pattern. Replace p and q with 12. Use the FOIL method to multiply. Multiply each side by 4. esolutions Manual - Powered by Cognero Page 4
5 15. TRIANGLES Find the dimensions of a triangle if the base is the measure of the height and the area is 12 square centimeters. 16. PATIO Eli is putting a cement slab in his backyard. The original slab was going to have dimensions of 8 feet by 6 feet. He decided to make the slab larger by adding x feet to each side. The area of the new slab is 120 square feet. Let b and h be the base and height of the triangle. a. Write a quadratic equation that represents the area of the new slab. b. Find the new dimensions of the slab. The height cannot be negative, so take h = 6 cm. a. b. The value of x cannot be negative, so. The dimensions of the slab are 12 feet by 10 feet. esolutions Manual - Powered by Cognero Page 5
6 Simplify The impedance in one part of a series circuit is 3 + 4j ohms and the impedance in another part of the circuit is 6 7j ohms. Add these complex numbers to find the total impedance in the circuit. esolutions Manual - Powered by Cognero Page 6
The equation of the axis of symmetry is. Therefore, the x-coordinate of the vertex is 2.
1. Find the y-intercept, the equation of the axis of symmetry, and the x-coordinate of the vertex for f (x) = 2x 2 + 8x 3. Then graph the function by making a table of values. Here, a = 2, b = 8, and c
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