Mathematics: Quadratic, Cubic, Distance-Time, and Velocity-Time Graphs, Exercises of Linear Algebra

Download Mathematics: Quadratic, Cubic, Distance-Time, and Velocity-Time Graphs and more Exercises Linear Algebra in PDF only on Docsity! QUADRATIC GRAPHS GRAPHS OF CIRCLES ‘The quadratic graph a curved shape called y Py oe ey =16(r= VI6 = 4) 34 | a parabola : yrax?+bxte vad LN on Ten + : Equation of a _| circle with a centre of (0, 0) and radius r / ; 35 | A positive x term will give aU shape z f/\\ x 4g aye / \ 36 | A negative (-x’) term will give a shape N The point where a curve turns in anieen ~~ the opposite direction f Gradient . = 37 | Turning points alias wainiav azide, ome A las a IEA = (x, ys) and B = (x2, ya) oe Ye » point between The gradient of line AB m = 222+ x 38 | useotsymmetry ee ae en enemeny rete Donte go | Perpendicular | When lines are perpendicular the product ofthe gradients is - 1.1 x 22 lines one graph has gradient m, the other has gradient — 2 39 Solution to the quadratic equation ax? + bx +¢ = 0 a. 40 | Roots The x-values where the graph crosses the x-axis Gradient of a_| The gradient (m) of a radius to a point [| she a1 A quadratic equation can have 0, 1, or 2 solutions Si | radius toa Scena eNees t¥ee crcle sz CUBIC GRAPHS = pres Isd yr vt Paxt3 DISTANCE ~ TIME GRAPHS ‘ A 52 | Represent a journey a [Pree tot text «53 | The vertical axis represents the distance from a . 2 ) will have 1,2, or 3 roots t}-—> +\—.: starting point i 54 | The horizontal axis represents time taken Z 55 | Straight lines mean constant speed Tie As steady speed, cnr 56 | Horizontal lines mean no movement anpiiosiieak Ee 7 57 | Gradient = speed C= steady speed back to start {3 | Reciprocal | where kis a numbe * cae 38 a _ Total distance |— functions —— ae erage speed = “Total time aa {It will have 2 asymptotes ‘VELOCITY ~ TIME GRAPHS. s Maximum and | 4 auadratic graph has a maximum point or Ce 59 | Represent the speed at a given time . minima | minimum point where the graph turns. | inmim_\ go | StBight ines mean constant , : ‘A cubic function contains an x° but no A acceleration/deceleration . 46 hi f 61 | Horizontal lines mean no change in velocit Tr ‘Otic Piher power af ‘\ mere teed Az steady acceleration, |__| functions con have an x! and xterm, : 62 | Positive Gradient = acceleration B = constant speed, a7 A cubic equation can have 1, 2, or 3 solutions 63 | Negative Gradient = deceleration C= steady deceleration back to 64 | The area under the graph = distance travelled astop