Aim: Review of Parabolas (Graphing)

Do Now: Write down the standard equation of a parabola

Answer: y = ax2 + bx + c

Homework: (Workbook) pg 427 (Part A+B only) #s 1,2,3

DEFINITIONS

• Parabola equation- y = ax2 + 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=ax2

• 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=-(x2 ) +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.

X Y

-2 -14

-1 -7

0 -2

1 1

2 2

Solution cont.

y=-(x2 ) +4x-2

(0,0)

Practice Problem

• Which is the equation for the accompanying graph?

• Choose:y = x2 - 4 y = -x2 -2x - 4 y = x2- 2x - 4y = -x2 + 2x + 4

• Answer : y = x2- 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

Practice Problem

• What is the equation of the axis of symmetry  of the graph y = 3x2 + 12x - 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 = –2x2 + 12x, where y is the height of the arc h .

• Graph the parabola from x = 0 to x = 6