What characteristics are easily found when given a quadratic equation in Standard form and/or vertex form? Explain exactly how you determine the characteristics. i. e. In vertex form (h ,k) is the vertex of the parabola.
How do you change a quadratic equation in vertex form to standard form? ex: y = 2(x + 3)^2 -1
How do you change a quadratic equation in standard form to vertex form? ex: y= x^2 +16x +2

Step-by-step explanation:

a)

y=2(x + 3)^2-1

this equation is in vertex form,

it is:

vertically stretched by a factor of 2

left 3 units (f(x)=a*(x - h)^(2)+k, so if h is positive it was -(-h) before ot got simplified)

down 1 unit

thus, vertex is (-3,-1)

b)

you can change it to standard form (f(x)=ax^(2)+bx+c) by:

simply multiplying everything out:

y=2(x + 3)^2-1

y=2(x^(2)+6x+9)-1

y=2x^(2)+12x+18-1

y=2x^(2)+12x+17

c)

y=x^2+16+2

this equation is in standard form ,

you can change it to vertex form (f(x)=a*(x - h)^(2)+k by:

y=1(x-h)^2+k

h=-b/2a

h=-16/2(1)

h=-8

solve for k

y=x^2+16+2

since vertex is (h,k) lets plug in h for x to find k and just solve for y:

k=y=(-8)^2+16+2

k=y=64+16+2

k=y=82

k=82

now that we know the vertex, lets write the equation in vertex form:

y=a*(x - h)^(2)+k

y=1(x-(-8))^(2)+82

y=(x+8)^2+82

answer: f = 32.2m

step-by-step explanation: that is the answer