3 Completing the SquareTransform the equation so that the constant term c is alone on the right side.If a, the coefficient of the second-degree term, is not equal to 1, then divide both sides by a.Add the square of half the coefficient of the first-degree term, (b/2a)2, to both sides (Completing the square)
4 Factor the left side as the square of a binomial. Completing the SquareFactor the left side as the square of a binomial.Complete the solution using the fact that (x + q)2 = r is equivalent tox + q = ±r
5 Solve: a2 – 5a + 3= 0 Move the 3 to the other side a = 1 Complete the square, add (5/2)2FactorSolve
6 Solve: x2 – 6x - 3= 0 Move the 3 to the other side a = 1 Complete the square, add (3)2FactorSolve
7 Solve: 2y2 + 2y + 5 = 0 move the 5 to the other side divide both sides by 2 (a 1)Add (1/2)2 to both sidesFactorSolve
8 Solve: 7x2 – 8x + 3 = 0 move the 3 to the other side divide both sides by 7 (a 1)Add (4/7)2 to both sidesFactorSolve
25 ParabolaParabola is the set of all points in the plane equidistant from a given line and a given point not on the line. Parabolas have an axis of symmetry (mirror image) either the x-axis or the y-axis. and
26 ParabolaThe point where the parabola crosses it axis is the vertex. The graph is a smooth curve.
27 ParabolaThe graph of an equation having the formy – k = a(x - h)2has a vertex at (h, k) and its axis is the line x = h.
28 Graphy = x2Use the form y – k = a(x – h)2k= 0, h = 0, so the vertex is (0,0) and x = 0
40 GraphTo graph y = a(x – h)2, slide the graph of y = ax2 horizontally h units. If h > 0, slide it to the right; if h < 0, slide it to the left. The graph has vertex (h, 0) and its axis is the line x = h.
41 Graphy – 3 = ½x2Use the form y – k = a(x – h)2k= 3, h = 0, so the vertex is (0,3) and x = 0