Quadratic and Trig Graphs

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Presentation transcript:

Quadratic and Trig Graphs Learning Outcomes Revise solution of quadratic equation. Make tables of quadratic functions in order to make graphs. Investigate quadratics graphs. Given a series of equations and graphs, be able to match the correct equation with graph. Be able to draw graphs of y = sinx, y = cosx, y = tanx and recognise important features. Approx Time 8 – 10 periods

Quadratic Equations Quadratic & Trig Graphs Draw for -3 ≤ x ≤ 3 y a) y = x2 + 3x – 4 x -3 -2 -1 1 2 3 x2 3x - 4 y add x y b) y = 2x2 – 3x – 5 x -3 -2 -1 1 2 3 x2 -3x - 5 y add x

Solving Simultaneous Equations Graphically Quadratic & Trig Graphs Solving Simultaneous Equations Graphically Solve x2 + 5x – t = x + 2 simultaneously y = x2 + 5x – t curve y = x + 2 straight line To solve these equations (graphically) we must draw the curve y= x2 + 5x and the line y = x + 2 and find the points of intersection.

Solving Simultaneous Equations Graphically Quadratic & Trig Graphs Solving Simultaneous Equations Graphically Given the equations of a curve (original) yes 1. Check LHS is original Draw ‘y = RHS’ no 2. Change LHS to original no 3. Draw ‘y = change’

Solving Simultaneous Equations Graphically Quadratic & Trig Graphs Solving Simultaneous Equations Graphically i) Draw for -2 ≤ x ≤ 5 the graph y = x2 – 3x – 3 ii) Use the graph to solve the equations a) x2 – 3x – 3 = 0 b) x2 – 3x – 3 = 4 c) x2 – 3x + 1 = 0 y x -2 -1 1 2 3 4 5 x2 -3x - 3 y x

Solving Simultaneous Equations Graphically Quadratic & Trig Graphs Solving Simultaneous Equations Graphically ii) Use the graph to solve the equations a) x2 – 3x – 3 = 0 b) x2 – 3x – 3 = 4 c) x2 – 3x + 1 = 0 Check LHS is original Draw ‘y = RHS’ Change LHS to original ‘y = change’ yes no

Graph of Trigonometrically Functions Quadratic & Trig Graphs Graph of Trigonometrically Functions y = sin x x 30 60 90 120 150 180 210 240 270 300 330 360 sin x sin x 90 180 270 360 Use the above graph to solve a) sin x = 0.5 b) sin x = -0.3

Graph of Trigonometrically Functions Quadratic & Trig Graphs Graph of Trigonometrically Functions y = cos x x 30 60 90 120 150 180 210 240 270 300 330 360 cos x cos x 90 180 270 360

Graph of Trigonometrically Functions Quadratic & Trig Graphs Graph of Trigonometrically Functions y = tan x x 30 60 90 120 150 180 210 240 270 300 330 360 tan x tan x 90 180 270 360

Trig Graphs Quadratic & Trig Graphs Sketch basic trig graphs, know their key points and period (90, 1) Period = 360° y = sin x (0, 0) (180, 0) (360, 0) -1 ≤ y ≤ 1 (270, -1) (0, 1) (360, 1) y = cos x Period = 360° (90, 0) (270, 0) -1 ≤ y ≤ 1 (180, -1) y = tan x (45, 1) Period = 180° (360, 0) (0, 0) -∞ ≤ y ≤ ∞ (180, 0)

Quadratic & Trig Graphs Additional Notes

At the end of the topic I will be able to Quadratic and Trig Graphs Learning Outcomes: At the end of the topic I will be able to Can Revise Do Further Revise solution of quadratic equation. Make tables of quadratic functions in order to make graphs. Investigate quadratics graphs. Given a series of equations and graphs, be able to match the correct equation with graph. Be able to draw graphs of y = sinx, y = cosx, y = tanx and recognise important features.          