Graphs, (Sketching, Circles, Straight Lines, Stationary Points) Flashcards
What does a (y = x) graph look like?
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What does a (y = -x) graph look like?
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What does a (y = x^2) graph look like?
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What does a (y = -x^2) graph look like?
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What does a (y = x^3) graph look like?
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What does a (y = -x^3) graph look like?
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What is the equation for a straight line graph, and what do the symbols stand for?
y = mx + c y = y co-ordinate x = x co-ordinate m = gradient c = y-intercept
What is the Equation for the mid-point?
mp = (x1+x2/2) , (y1+y2/2)
What is the equation for the gradient of a line on a graph?
m = (y2-y1) / (x2-x1)
What is the gradient of parallel and perpendicular lines?
Parallel = same gradient Perpendicular = -1/m
How do you find the distance between two points on a graph?
d = /(x2 – x1)^2 + (y2 – y1)^2
What are the equations for direct and inverse proportion?
Direct Proportion: y = kx
Inverse Proportion: y = k/x
What is a circle?
A 2D line where all the points are equidistant from the centre
How do you find the equation of a tangent of a circle?
- Find the gradient of AB
- Work out the perpendicular gradient
- Find the co-ordinate of the centre
- Find the equation
What is the equation for a circle?
(x – a)^2 + (y – b)^2 = r^2
(a, b) = centre of the circle
r = radius
How do you check if a circle passes through a certain point?
Substitute the equations for (x,y)
How do you find where the circle meets the x axis?
Sub y for 0
How do you find where the circle meets the y axis?
Sub x for 0
How do you find where the circle meets the line?
Sub the line equation in the circle equation
What does it mean if there are no (x,y) when you sub in the line equation?
Line doesn’t intercept circle
What does it mean if there is 1 (x,y) when you sub in the line equation?
Line intercepts circle once
What does it mean if there is 2 (x,y) when you sub in the line equation?
Line intercepts circle twice
What is the gradient at stationary points?
m = 0
How do you find the stationary point(s)?
- Differentiate
- Solve to = 0
- Substitute
How do you find out if the stationary point is a maximum or a minimum?
d^(2)y / dx^2
Substitute in co-ordinates
Positive = minimum
Negative = maximum
What does a (y = x^4) graph look like?
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What does a (y = -x^4) graph look like?
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What does a (y = 1/x) graph look like?
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What does a (y = -1/x) graph look like?
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What does a (y = 3/x) graph look like?
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