Chapter 10 Study Notes x2 2x 3= y – – How do I find? If the parabola Is a negative or Negative Positive opens up or positive? The parabola opens down! The parabola opens up! down? If the parabola Is a negative or Negative Positive has a minimum positive? Parabola has a maximum. Parabola has a minimum. or maximum? Axis of After finding a, b, and x = x = Symmetry c; use b and a in the x = 1 a.o.s. equation (, Vertex After finding the axis x2 2x 3= y – – the value for x plugged into of symmetry, use that (1)2 2(1) 3= y – – the equation) value for x and plug 1 2 3 =y – – the value for x into -4 = y the equation to get y. The vertex is the point (1, -4) The number of Use the discriminant! (-2)2 1) (-3) –4( roots of a b2 a c 4 (-12) –4 – quadratic If the discriminant is 16 equation positive 2 roots (positive) – Zero 1 root – Negative 0 roots There are 2 roots – Roots using Factor using methods Use your factor sheet or the x2 2x 3 – – factoring from Method” (x 3)(x + 1) “Riley – Chapter 9. (x 3) = 0 (x + 1) = 0 or – Set each factor = 0 x = 3, -1 using the Zero Product Property.
Chapter 10 Study Notes x2 – 2x – 3= y How do I find? If the parabola opens up or down? Is a negative or positive? Negative The parabola opens down! Positive The parabola opens up! If the parabola has a minimum or maximum? Is a negative or positive? Negative Parabola has a maximum. Positive Parabola has a minimum. Axis of Symmetry a.o.s. After finding a, b, and c; use b and a in the equation x = x = x = 1 Vertex After finding the axis of symmetry, use that value for x and plug the value for x into the equation to get y. (, the value for x plugged into the equation) x2 – 2x – 3= y (1)2 – 2(1) – 3= y 1 – 2 – 3 =y -4 = y The vertex is the point (1, -4) The number of roots of a quadratic equation Use the discriminant! If the discriminant is positive – 2 roots Zero – 1 root Negative – 0 roots b2 –4 a c (-2)2 –4( 1) (-3) 4 – (-12) 16 (positive) There are 2 roots Roots using factoring Factor using methods from Chapter 9. Set each factor = 0 using the Zero Product Property. Use your factor sheet or the “Riley Method” x2 – 2x – 3 (x – 3)(x + 1) (x – 3) = 0 or (x + 1) = 0 x = 3, -1
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