Quadratic graphs 0.0 / 5 ? MathematicsGraphs and transformationsA2/A-levelAQA Created by: Ice_FoxCreated on: 29-09-21 11:28 Sketch a quadratic (3 marks) 1 mark - shape of the curve 1 mark - coordinates of the x and y intercepts 1 mark - coordinates of the min/max 1 of 6 The shape of the curve Quadratic - parabola - u shape if the coefficient on x^{2 }is positive - n shape if the coefficient on x^{2 }is negative 2 of 6 Coordinates of the x and y intercepts Y-intercept - substitute x=0 into the equation - e.g. y = ax^{2 }+ bx + c y = 0x^{2 }+ 0x + c y = c X-intercepts - substitute y=0 into the equation - e.g. y = x^{2 }+ 5x + 6 0 = x^{2} + 5x + 6 0 = (x + 3) (x + 2) x = -3 OR x = -2 3 of 6 Number of real roots Put it in the form: ax^{2 }+ bx + c =0 The disciminant: b^{2 }- 4ac If... b^{2 }- 4ac > 0 it has 2 distinct real roots / crosses the x-axis twice b^{2} - 4ac = 0 it has 1 real root (or two repeated roots) / crosses the x-axis once b^{2 }- 4ac < 0 it has no real roots / never crosses the x-axis 4 of 6 Coordinates of min/max Positive coefficient on x^{2 } = Minimum Negative coefficient on x^{2 } = Maximum To find min/max: - complete the square - e.g. (x - p)^{2 }+ q - Min/Max = (p, q) 5 of 6 Line of Symmetry Complete the square: (x - p)^{2 }+ q The line of symmetry: x = p 6 of 6

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