# Parabolas

### Important parts of the parabola

## Vertex/Axis of Symmetry

**Vertex:**Maximum or Minimum point of a parabola

**Axis of Symmetry**: Vertical line going through the vertex (x value of the vertex point)

**To find the axis of symmetry (x value of vertex)**

1. Quadratic needs to be foiled out into standard form

2. x = -b/2a

3. Once you have the x value, plug into the equation to calculate the y value of the vertex

## Parabola Parts

## How to write an Equation of A Parabola

## Steps:

- Given x intercepts of (2, 0) and (-3,0)

- y = (x - 2)(x + 3)

2. Given direction graph opens:

- Upward = a
- Downward = -a
- y = a(x - 2)(x + 3)

3. Given a min/max point (vertex!):

- We are looking for 'k' (it will go in front of factored quadratic)

- Write out intercepts like step 1: y = (x -2) (x + 3)
- Given the maximum or minimum point (plug in x and y and solve for k)

12.5 = k [ (-0.5 - 2) (-0.5 + 3) ]

12.5 = k [ (-2.5)(2.5)]

12.5 = k [-6.25]

12.5 = -6.25k

k = -2

- So: a parabola with x-intercepts of 2 and -3 with a maximum of (-0.5,12.5) will have an equation of: y = -2(x - 2)(x + 3)

Test it on your calculator!