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Curves Dr Duxbury
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Are the following quadratic functions?
Quadratic graphs In a quadratic function, the highest power of x is 2 and it is of the form y = ax2 + bx + c. Are the following quadratic functions?
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Cubic graphs In a cubic function, the highest power of x is 3 and it is of the form y = ax3 + bx2 + cx + d. Are the following cubic functions?
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Drawing a quadratic graph
Plot the following quadratic function: What do we do first?
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Set up a table finding points which are on the curve:
x -3 -2 -1 1 2 3 x2 -3x y
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Set up a table finding points which are on the curve:
x -3 -2 -1 1 2 3 x2 9 4 -3x y x -3 -2 -1 1 2 3 x2 -3x y
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Set up a table finding points which are on the curve:
x -3 -2 -1 1 2 3 x2 9 4 -3x 6 -6 -9 y x -3 -2 -1 1 2 3 x2 -3x y x -3 -2 -1 1 2 3 x2 9 4 -3x y
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Set up a table finding points which are on the curve:
x -3 -2 -1 1 2 3 x2 9 4 -3x y x -3 -2 -1 1 2 3 x2 9 4 -3x 6 -6 -9 y x -3 -2 -1 1 2 3 x2 9 4 -3x y x -3 -2 -1 1 2 3 x2 -3x y
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Set up a table finding points which are on the curve:
x -3 -2 -1 1 2 3 x2 9 4 -3x y 20 12 6 x -3 -2 -1 1 2 3 x2 9 4 -3x y x -3 -2 -1 1 2 3 x2 9 4 -3x y x -3 -2 -1 1 2 3 x2 -3x y x -3 -2 -1 1 2 3 x2 9 4 -3x 6 -6 -9 y
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Plot the points and join them up:
y x
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Plot the points and join them up:
y x
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Plot the points and join them up:
y x
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Plot the points and join them up:
y x
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Drawing a quadratic graph II
Checking your graph looks right: x -3 -2 -1 1 2 3 y 20 x -3 -2 -1 1 2 3 y 20 x -3 -2 -1 1 2 3 y 12 20 x -3 -2 -1 1 2 3 y 20 x -3 -2 -1 1 2 3 y 20 x -3 -2 -1 1 2 3 y 6 20
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Plot the points and join them up:
y x
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Plot the points and join them up:
y x
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Graphical Solution of Equations
Solve Let Then find the values of x where the curve cuts the x-axis (that is where y=0).
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Graphical Solution of Equations
If we were to solve this equation without using a graph, then we could factorise the equation: To solve it graphically:
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The roots of a quadratic equation
Solve x2 + 2x – 3 = 0 y x = -3 x = 1
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The roots of an equation
This tells us that the solution to the equation is
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Graphical Solution of Equations
Solve
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The roots of a quadratic equation
y Solve x2 + 2x – 3 = -2 So x = -2.5 and 0.5 x = -2.5 x = 0.5 y = -2
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Exercise: Plot the graph of y = x2 +3x – 4
for values of x between –5 and 2 Use your graph to find values of x such that x2 +3x – 4 = 0, x2 +3x – 4 = -4 and x2 +3x – 4 = x
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Solution y = 0
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Solution y = -4
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Solution y = x
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