Graphing a Quadratic Equation – The Parabola Format of a general quadratic equation: ax2 + bx + c = 0 Format of a parabola: y = ax2 + bx + c

Graphing a Quadratic Equation – The Parabola To graph a parabola: y = ax2 + bx + c First, find the “Axis of Symmetry.” (AOS) Use the formula: x = -b 2(a) The axis of symmetry gives you the x-coordinate of the turning point. To find the y-coordinate of the turning point, plug the x-coordinate back in to the equation If you solved the parabola for zero, this would give you the roots of the equation

Graphing a Quadratic Equation – The Parabola To graph a parabola: Create a table – balanced around the axis of symmetry X Y AOS Value Y-Coordinate of Turning Point

Graphing a Quadratic Equation – The Parabola Example 1: Nice and Easy y = x2 – 4x - 5 Find the Axis of Symmetry and the Turning Point. Try to find Roots Complete Table Graph Parabola X Y

Graphing a Quadratic Equation – The Parabola Example 2: Downward Parabola y = -x2 – 6x + 7 Find the Axis of Symmetry and the Turning Point Try to find roots Complete Table Graph Parabola X Y

Graphing a Quadratic Equation – The Parabola Example 3: When the Turning Point is NOT an Integer y = x2 + 5x - 1 Find the Axis of Symmetry and the Turning Point Try to find roots Complete Table Graph Parabola X Y

Graphing a Quadratic Equation – The Parabola Example 4: When Given a Specific Interval y = x2 – 4x + 3 (-1≤ x ≤ 5) If given an interval, DON’T HAVE TO FIND the Axis of Symmetry and the Turning Point Don’t need to find roots Complete Table (x-values are given) Graph Parabola X Y

Graphing a Quadratic Equation – The Parabola Example 5: When Given the the Picture of a Parabola Use the picture to find the roots Work backwards from the roots to create factors. Multiply the factors to create the parabolic equation Make sure your equation says y =