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Quadratic Equations

Pg 1 of 5. Quadratic Equations. Investigate what the following quadratics look like Y = A X 2 Y = AX 2 + C Y = A(X -B ) 2 Y = (X – A)(X - B). Pg 2 of 5. Y= A X 2. Y = + A X 2 is a “ happy ” curve which turns on the x axis and has a line of symmetry which is X=0.

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Quadratic Equations

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  1. Pg 1 of 5 Quadratic Equations Investigate what the following quadratics look like Y = AX2 Y = AX2+ C Y = A(X-B)2 Y = (X – A)(X - B)

  2. Pg 2 of 5 Y= A X2 Y = +A X2 is a “happy” curve which turns on the x axis and has a line of symmetry which is X=0. This curve has a min turning pt. The bigger the (co-efficient) value of A the narrower the curve. Eg y = 5x2 Y = - A X2 is an “unhappy” curve which turns on the x axis and has a line of symmetry which is X = 0. This curve has a max turning pt. Again, the larger the co-efficient the narrower the graph. Eg y = -3x2

  3. Y = A X2 + C Pg 3 of 5 Y = AX2 + C is a curve which has X = 0 as a line of symmetry. The + C shifts the curve up by the value of C if the sign is positive and down by the value of C if the sign is negative.

  4. Pg 4 of 5 Y = A(X-B)2 Y = A(X-B)2 is a curve which is moved horizontally by the amount B. If the sign is negative the curve would be shifted to the right. Eg Y = (X-2)2 If the sign is positive the curve would be shifted to the left. Eg Y = (X+3)2

  5. Pg 5 of 5 Y = (X-A)(X-B) Y = (X-A)(X-B) is another form of the quadratic equation. The roots of the equation are where the curve cuts the x axis. The axis of symmetry is in the middle of where the roots cut the x axis. Eg (-4,0) and (2,0) has an axis of symmetry X= - 1. The turning point is called the vertice. In this example the vertice appears at x = - 1. To find the point sub x = - 1 into the equation. Y = (-1-2)(-1+4) Y = (-3)(3) Y = -9 So the vertice is (-1 , -9) ROOTS Minimum turning point

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