COMMUNICATION QUESTION:

Question

COMMUNICATION QUESTION:

There are 3 forms of a quadratic equation....standard form, vertex form and factored form. In this question, I want you to list ALL the ways that you now know about changing from one form to another (and explain BRIEFLY how to make that change) Here is one for your list..... To change from factored form to standard form you need to expand and simplify (use "FOIL" and distributive property) 

Answer 1

standard form: ax^2 + bx + c, c= the y intercept

vertex form: a(x-h)^2 + k where (h,k) = the vertex

factored form: a(x-d)(x-e) where d and e are zeros or x intercepts

convert standard to vertex form:

ax^2 + bx + c

= a(x^2 +bx/a) + c,

complete the square

= a(x^2 + bx/a + (b/2a)^2) + c - a(b/2a)^2

= a(x + b/2a)^2 + c-a(b^2/4a^2)

= a(x+b/2a)^2 + c-(b^2/4a)

= a(x+b/2a)^2 + (4ac-b^2)/4a

where (-b/2a, (4ac-b^2)/4a) is the vertex of the parabola, = maximum of a<0, minimum if a>0

notice the numerator of the y coordinate = the negative of the discriminant

and the x coordinate is the negative of the 1st term of the solution for x using the quadratic formula

x = -b/2a + or - (1/2a)sqr(b^2 - 4ac)

factor form:

a(x-d)(x-e)

= a(x^2 -(d+e)x +de)

=ax^2 -a(d+e)x + ade

where ad+ae = b and ade = c

for standard form ax^2 + bx + c

= ax^2 +(ad+ae)x + ade