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Graphs

Graphs. Types of equations. Linear ( straight line) : highest power of x is 1 Parabolic ( quadratic) : highest power of x is 2 Cubic : y = highest power of x is 3 Reciprocal ( two part graph) : x is in the denominator. Straight line graphs ( no turning point).

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Graphs

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  1. Graphs

  2. Types of equations • Linear ( straight line) : highest power of x is 1 • Parabolic ( quadratic) : highest power of x is 2 • Cubic : y = highest power of x is 3 • Reciprocal ( two part graph) : x is in the denominator

  3. Straight line graphs ( no turning point)

  4. Quadratic graphs ( one turning point)

  5. Quadratic graphs

  6. Quadratic graphs

  7. Quadratic graphs

  8. Quadratic graphs

  9. Cubic ( two turning points)

  10. Cubic graph

  11. Cubic graph • The y intercept is still the point where the graph hits the y axis ( the number which is by itself in the equation)

  12. Reciprocal graphs

  13. Intersecting graphs • Consider the graphs of y =x^2 + x -2 and y = x + 1 • The points where they meet are called the points of intersection. • In this case they are (-1.7, -0.7) and (1.7, 2.7)

  14. Intersecting graphs • Sometimes you can be asked for a range. • Example: Give the range of x values such that x^2 + x – 2 < x + 1 • This means you need to find the values of x for which the curve is smaller than the line. • In this case -1.7 < x < 1.7

  15. Intersecting graphs • You might also be asked to find the range of x such that x^2 + x – 2 > x + 2 • This means the values of x such that the curve is higher than ths line • In this case you have two distinct ranges • x < -1.7 and x > 1.7 • Obviously you add the line underneath • the inequality if it is needed.

  16. Intersecting graphs • When a cubic graph intersects a straight line graph, you may have 3 points of intersection. • In this case the points are: • (-4.8, 2.8), ( -2,0) and ( 0.8,2.8)

  17. Intersecting graphs • Give the range of values such that the cubic < straight line • x < -4.8 and -2 < x < 0.8

  18. Equations of intersecting graphs • You have been asked to plot the graph of y = x^2 + 2x -3. • Then you are asked • “ By plotting a suitable graph, solve the equation x^2 + x – 1 = 0” • You need to get the new equation to resemble the old one.

  19. Intersecting graphs • First, take the new equation and write it down. • x^2 + x – 1 = 0 Then, take whatever is different from the old one to the other side. x^2 = -x + 1 Then, add the terms which will make it like the old one x^2 + 2x – 3 = -x + 1 +2x – 3 Make sure that you put them on both sides x^2 + 2x – 3 = x – 2 Simplify and plot the equation on the right. The solution will be the x values of the points of intersection of the two graphs.

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