This week in math, we learned more about quadratic functions and how to find the x intercepts through factored form. We learned through general form we can find the y intercept and through standard form we can find the vertex and the axis of symmetry. Taking this information, we can take the general form of the equation and convert it into either standard form or factored form to find the information that we need.

General form:

Standard form(completing the square): +

Factored form: = () ()

Ex) General form to factored and standard form

= 2 -14 + 16

- y-intercept: 16
- opens up, minimum value
- congruent: =2
- stretches

= (2-16) (+1)

- x-intercepts: (8, 0) (-1, 0)
- axis of symmetry(x) = 3.5

= 2 -14 + 16

= 2( -7+49/4 -49/4)+ 16

= 2( -7+49/4)-98/4+ 64/2

= 2( -7/2)^{2} -34/4

= 2( -7/2)^{2} -17/4

- vertex (3.5, 8.5)