Quadratic Equations Investigate what the following quadratics look like Y = AX 2 Y = AX 2 + C Y = A(X-B) 2 Y = (X – A)(X - B) Pg 1 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. This curve has a min turning pt. The bigger the (co-efficient) value of A the narrower the curve. Eg y = 5x 2 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 = -3x 2 Pg 2 of 5

Y = A X 2 + C Y = AX 2 + 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. Pg 3 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 Pg 4 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 Pg 5 of 5