3x+2y=6 -
8x+2y=2
_________
-5x=4
x=-4/5
-2.4+2y=6
y=8.4
The system shown at the right has no solution, as the grahs never intersect.
On the other hand, the line and the parab. at the left do intersect, and the points of intersection are (-3,0) and (6,6).
Answer: see below
<u>Step-by-step explanation:</u>
The vertex form of a quadratic equation is: y = a(x - h)² + k where
- "a" is the vertical stretch (positive = min [U], negative = max [∩])
- (h, k) is the vertex
- Axis of Symmetry is always: x = h
- Domain is always: x = All Real Numbers
- Range is y ≥ k when "a" is positive or y ≤ k when "a" is negative
a) y = 2(x - 2)² + 5
↓ ↓ ↓
a= + h= 2 k= 5
Vertex: (h, k) = (2, 5)
Axis of Symmetry: x = h → x = 2
Max/Min: "a" is positive → minimum
Domain: x = All Real Numbers
Range: y ≥ k → y ≥ 5
b) y = -(x - 1)² + 2
↓ ↓ ↓
a= - h= 1 k= 2
Vertex: (h, k) = (1, 2)
Axis of Symmetry: x = h → x = 1
Max/Min: "a" is negative → maximum
Domain: x = All Real Numbers
Range: y ≤ k → y ≤ 2
c) y = -(x + 4)² + 0
↓ ↓ ↓
a= - h= -4 k= 0
Vertex: (h, k) = (-4, 0)
Axis of Symmetry: x = h → x = -4
Max/Min: "a" is negative → maximum
Domain: x = All Real Numbers
Range: y ≤ k → y ≤ 0
d) y = 1/3(x + 2)² - 1
↓ ↓ ↓
a= + h= -2 k= -1
Vertex: (h, k) = (-2, -1)
Axis of Symmetry: x = h → x = -2
Max/Min: "a" is positive → minimum
Domain: x = All Real Numbers
Range: y ≥ k → y ≥ -2
