Aim: Review of Parabolas (Graphing) Do Now : Write down the standard equation of a parabola Answer: y = ax 2 + bx + c Homework: (Workbook) pg 427 (Part.

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Aim: Review of Parabolas (Graphing) Do Now : Write down the standard equation of a parabola Answer: y = ax 2 + bx + c Homework: (Workbook) pg 427 (Part A+B only) #s 1,2,3

DEFINITIONS Parabola equation- y = ax 2 + bx + c Axis of Symmetry- The axis of symmetry is the line x = -b/2a Parabola definition- A parabola is the set of all points (x,y) that are the same distance from a fixed line (called the directrix) and a fixed point (focus) not on the directrix. Equation of a parabola with vertex at 0,0- y=ax 2 Vertex of a parabola- minimum (lowest) or maximum (highest) value of the parabola

Parabola (Max;Min) Parabolas are of the form: y = ax2 + bx + c If a is positive, the parabola opens upward and has a minimum point. The axis of symmetry is x = (-b)/2a If a is negative, the parabola opens downward and has a maximum point. The axis of symmetry is x = (-b)/2a.

Graph this parabola y=-(x 2 ) +4x-2 Solution: Find the Axis of Symmetry- Plug in the answer for x and solve for y Plug in more values for x and construct a table. XY

Solution cont. y=-(x 2 ) +4x-2 (0,0)

Practice Problem Which is the equation for the accompanying graph? Choose: y = x y = -x 2 -2x - 4 y = x 2 - 2x - 4 y = -x 2 + 2x + 4 Answer : y = x 2 - 2x - 4

Practice Problem What is the equation of the axis of symmetry for this parabola? (Hint: You do not need to use Axis of Symmetry equation) Answer : X=1

What is the equation of the axis of symmetry of the graph y = 3x x - 2 ? Answer : X=-2

Regents problem An arch is built so that it is 6 feet wide at the base. Its shape can be represented by a parabola with the equation y = –2x x, where y is the height of the arc h. Graph the parabola from x = 0 to x = 6