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Quadratic theory Part 2 Unit 2

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Equations from graphs and related graphs

If a graph crosses the x axis at (a,0) and (b,0) the equation of the graph must be of the form y=k(x-a) (x-b) for some value of k. You'll need to find k from additional information. You may be given the turning point, or a point on the y{}{}{}{} axis, for example, so to find k substitute these co-ordinates into the equation above.

Follow our working to find the equation of the parabola shown.

Graph of y = 10 + 8x - 2xsquared

Graph of y = 10 + 8x - 2xsquared

 

roots at -1 and 5 => y = k (x + 1)(x - 5) for some value of k

(remember that for a maximum turning point, k is negative)

substituting the co-ordinates of (0, 10) => 10 = k (1)(-5) => k = -2

hence y = -2 (x + 1)(x - 5) = 10 + 8x - 2x^2.

Find the equation of the parabola shown.

Graph of y= 3x squared - 12x

Graph of y= 3x squared - 12x

 

roots at 0, 4 => y = k (x)(x - 4) for some value of k

(remember that the turning point is halfway between the roots)

substituting the co-ordinates of (2, -12) => -12 = k(2)(-2) => k = 3

hence y = 3 x (x - 4) = 3x^2 - 12x

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