Question

Part 1 − Find the vertex, axis of symmetry, domain, and range of the graph of y = −2x2 − 6x + 1. Show all work for full credit.

Answer 1

y = −2x2 − 6x + 1
factoring then completing the square
y = -2(x^2 + 3x -1/2) = -2[(x+3/2)^2 -(3/2)^2 -1/2]
y = -2[(x+3/2)^2 -13/4]
from this you can see it open down, vertex at -3/2, shifted down -13/4 if my arithmetic is correct

Answer 2

Thank you!

Answer 3

how about Create your own quadratic equation that has an axis of symmetry of x = 1 and whose graph opens down. Then find the vertex, domain, range, and x-intercepts. Show all work to receive full credit.

Answer 4

y = -(x-1)^2 + b
vertex x = 1
- implies open down
b is elevation of parabola, y, at x =1
domain x = all real number
range y = all real number

Answer 5

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

Answer 6

What is the domain of the graph of y = −2x2 − 4x + 7?

Answer 7

the domain is all number which x can take on, if this case
-infinity to +infinity
range is all numbers of x for which y is defined, in this case the same

Answer 8

actually not true for range, the values y takes on for all x
y = −2x2 − 4x + 7 = -2((x+1)^2 + 9
Domain all real numbers
Range y < or = 9