Algebra I Module 8 Quadratic Tutorial 2013

A Quadratic function f is a function in the form: f(x) = ax ^{2} + bx + cwhere a,b and c are real numbers. ex. f(x) = 2x ^{2} + 4x + 10a = 2, b = 4 and c = 10 a = a = In the equation y = 6x ^{2} - 3x + 8What are the values of a, b and c? In the equation y = 4x ^{2} + 2x + 1What are the values of a, b and c?b = b = c = c = Parabolas are "u" shaped graphs that open upward or downward and are vertically symmetrical. The lowest or highest point of a parabola is called the vertex. It is the point where the curve changes directions. The vertex is also a point on the axis of symmetry. The axis of symmetry is an imaginary line that vertically goes through the axis. For this quadratic the vertex is (3, 4) and the axis of symmetry is x = 3 Notice that the axis of symmetry is really just the x value. (3, 4) x =3 The vertex of this parabola is ( , ) The axis of symmetry is x = All other quadratics are derived from this. The parent function of a quadratic is y = x ^{2}If the "a" term of the a quadratic, or coefficient of the squared term, is positive, the parabola opens upward creating a minimum vertex. If the "a" term of the quadratic is negative, the parabola opens downward creating a maximum vertex. In the equation y = 4x ^{2} + x - 20, the "a" termis positve 4. Therefore the parabola opens upward and has a minimum vertex. In the equation y = -3x ^{2} +10x +3, the "a" termis negative 3. Therefore the parabola opens downward and has a maximum vertex. In the equation, y = 10x ^{2} - 3x - 4, which of the following are true: the parabola opens upward with max. vertex the parabola opens upward with min. vertex the parabola opens downward with max. vertex the parabola opens downward with min. vertex |

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