07 sketching graphs - flatter at base steeper at the...

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Sketching Graphs * Numbers on axes must be evenly spaced * y intercept occurs when x = 0 * x intercept occurs when y = 0 Once the intercepts have been found, curves are easy to sketch, if you know the basic shape. If in doubt use a table of values and plot some points
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Basic Curves b mx y + = x y = c bx ax y + + = 2 1 ` power 0 solve 2 = + + c bx ax (1) Straight Lines y x 1 ` power (2) Parabola y x 2 x y = 1 ` power 2 ` power x intercepts: vertex: halfway between x intercepts
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e.g. find the x intercepts and vertex of 3 4 2 + - = x x y ( 29 1 2 2 - - = x y ( 29 1 , 2 vertex - ( 29 1 2 2 = - x x intercepts: 1 2 1 2 ± = ± = - x x x = 1 or x = 3 y x 1 ( 29 1 , 2 - 3 (3) Cubic y x 3 x y = d cx bx ax y + + + = 2 3 1 ` power 3 ` power ( 29 cubic. basic the like look it will then to factorised be can it If 3 k x a y + = Otherwise; y x
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(4) Higher Powers y x etc even 6 4 x y x y = = y x etc odd 7 5 x y x y = = As power gets bigger, curve gets;
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Unformatted text preview: - flatter at base- steeper at the sides (5) Hyperbola y x 1 1 = = xy OR x y x y 1 = one power on top of a fraction, one power on bottom of fraction (6) Circle y x 2 2 2 r y x = + y x ( 29 1 = a a y x (7) Exponential 2 2 2 r y x = + r r-r-r both power ‘2’ coefficients are the same x a y = pronumeral in the power 1 (8) Roots y x 2 2 x r y-= y x x y = r r-r to tell what the curve looks like, square both sides circle 2 2 2 2 2 2 2 2 ∴ = +-=-= r y x x r y x r y parabola 2 ∴ = = x y x y half top means + half bottom means-Exercise 2G; 1adeh, 2adgk, 3bdf, 5aeh, 7acegi, 8ad, 9a, 11c, 13acd, 15bd, 17*...
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07 sketching graphs - flatter at base steeper at the...

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