A function is defined as f(x) = -x2 + 9. The points A and B are the x-intercepts, and C is the y-intercept. Find the length of AB, the coordinates of C, and the equation of the line passing through B

Okay 🥹❤️‍🔥M💞🥹Miseketeri, let's tackle Question 4. Question 4.1: Determine the length of AB. Step 1: Find the x-intercepts of f(x). The x-intercepts occur when f(x) = 0. -x^2 + 9 = 0 x^2 = 9 x = ±sqrt(9) x = ± 3 Step 2: Identify points A and B and calculate the length. From the diagram, A is the negative x-intercept and B is the positive x-intercept. So, A is (-3, 0) and B is (3, 0). The length of AB is the distance between these two points. Length AB = 3 - (-3) = 3 + 3 = 6 The length of AB is 6 units. Question 4.2: Determine the coordinates of C. Step 1: Find the y-intercept of f(x). The y-intercept occurs when x = 0. f(0) = -(0)^2 + 9 f(0) = 9 The coordinates of C are (0, 9). Question 4.3: Determine the equation of the straight line g(x). Step 1: Identify two points on the line g(x). The problem states that g(x) passes through B and C. From 4.1, B is (3, 0). From 4.2, C is (0, 9). Step 2: Calculate the slope (m) of the line. m = (y_2 - y_1)/(x_2 - x_1) = (9 - 0)/(0 - 3) = (9)/(-3) = -3 Step 3: Determine the y-intercept (c) and write the equation. The y-intercept is the y-coordinate of point C, which is 9. So, c = 9. The equation of the straight line g(x) is g(x) = -3x + 9. Question 4.4: Determine the distance of DF if OD = 5 units. Step 1: Identify the coordinates of D. Given that OD = 5 units and D is on the x-axis, the coordinates of D are (5, 0). Step 2: Determine the coordinates of F. Assuming F is the point on the parabola f(x) with an x-coordinate of 5 (consistent with D(5,0) and DE being parallel to the y-axis). f(5) = -(5)^2 + 9 f(5) = -25 + 9 f(5) = -16 So, the coordinates of F are (5, -16). Step 3: Calculate the distance DF. Since D and F have the same x-coordinate, the distance DF is the absolute difference of their y-coordinates. Distance DF = |0 - (-16)| = |16| = 16 The distance of DF is