Answer:
Step-by-step explanation:
The given equation of a parabola is,
[tex]y=-\frac{1}{2}(x+3)^2+4[/tex]
When we compare this equation with the vertex form of the quadratic equation,
y = a(x - h)² + k
where (h, k) is the vertex,
Vertex of the parabola,
(-3, 4)
y-intercept,
[tex]y=-\frac{1}{2}(0+3)^2+4[/tex]
[tex]y=-\frac{9}{2}+4[/tex]
[tex]y=-\frac{1}{2}[/tex]
x-intercepts,
[tex]0=-\frac{1}{2}(x+3)^2+4[/tex]
[tex]\frac{1}{2}(x+3)^2=4[/tex]
(x + 3) = ±√8
x = (3 - 2√2), (3 + 2√2)
Axis of symmetry,
x = -3
Domain:
(-∞, ∞)
Range:
(-∞, 4]
