Question Solve each of the following inequalities: a. b. Solution a. We are given; b. We are given; First we find the critical values for this inequality. Therefore; Now we have two options. Standard form of quadratic equation is; The graph of quadratic equation is a parabola. If (‘a’ is positive) then parabola opens upwards and its vertex […]
Question a. Express in the form . b. A curve has equation . Using your answer form part (a), or otherwise: i. Find the coordinates of the vertex (minimum point) of the curve. ii. Sketch the curve, indicating the value where the curve crosses the y-axis. c. Describe geometrically the […]
Question a. Simplify b. The quadratic equation has real roots. i. Show that ii. Hence find the possible values of . Solution a. We are given; b. i. We are given that following quadratic equation has real roots. For a quadratic equation , the expression for solution is; Where is called discriminant. If , the equation […]
Question The diagram below shows a rectangular sheet of metal 24 cm by 9 cm. A square of side x cm is cut from each corner and the metal is then folded along the broken lines to make an open box with a rectangular base and height x cm. a. Show that the volume, cm3, of liquid the […]
Question A circle has equation . a. By completing the square, express the equation in the form b. Write down: i. the coordinates of the center of the circle; ii. the radius of the circle c. The line with equation intersects the circle at the points P and Q. i. Show that the x-coordinates of P and Q satisfy the equation […]