Quadratic formulas

a) what is the effect on the graph of f(x) if it is changed to f(x) + 7 and f(x + 7)? (mp 6, 7)

b) give an example of how you would solve an equation by completing the square. describe the steps.

c) describe the process of graphing a quadratic equation without using graphing technology. (

A.
moving a graph up c units, add c to whole function
moving a graph v units to the right, minus v from every x
f(x)+7 moves the whole function up 7 units
f(x+7) moves the graph 7 units to the left

B.
first, gropu x terms
2nd, factor out 2nd degree coefient
3rd, take 1/2 of linear coefient and squre it,
4th add negative and positive inside parnthasees
5th factor perfect square
6th distribute
7th, add like terms
8th minus constatnt oto move onto opostie side
9th, divide by factor of the sqrt thing
10th sqrt both sides,. remember positive and negative roots
11th minus constant to isolate x

example
2x^2+8x-5=0
group x terms
(2x^2+8x)-5=0
factor out x^2 term coefient
2(x^2+4x)-5=0
take 1/2 of linear coefient (4) and square it
4/2=2, 2^2=4
add negatie and positive inside
2(x^2+4x+4-4)-5=0
factor perfect square
2((x+2)^2-4)-5=0
distribut
2(x+2)^2-8-5=0
add like terms
2(x+2)^2-13=0
add 13 oth sides
2(x+2)^2=13
divide both sides by 2
(x+2)^2=13/2
sqrt both sides, don't forget negative and positive roots
x+2=+/-√(13/2)
minus 2 both sides
x=-2+/-√(13/2)
x=-2+√(13/2) and -2-√(13/2)

C. find the vertx by completing the square and getting into form
y=a(x-h)^2+k
(h,k) is the vertex
if a is positive, the parabola opens up
if a is neative, the the parabola opens down
after plotting the vertex, plot some points by subsitution