+118725 Graph the function: Y=x^2+4x+3..
Vertex:
Axis of Symmetry:
Domain:
Range:
\(y=x^2+4x+3\)
This is a parabola because it is a polynomial of degree 2 (The highest power of x is 2)
There is an invisable +1 in front of the x^2 (1 is the leading coefficient)
Since the leading coefficient is positive the parabola is concave up.
\(y=x^2+4x+3\\ y=(x+3)(x+1)\\ \)
The roots of the parabola are where y=0
y will equal zero when x+3=0 and when x+1=0
roots are x = -3 and x = -1
The axis of symmetry will be half way between the roots
x=(-3+-1)/2 = -4/2 = -2
Axis of symmetry is x = -2
When x=-2 y=2^2-4*2+3 = 4 -8 +3 = -1 So the vertex is (-2, -1)
Domain: \(x \in Z\) (x can be anything)
Range: \(y\ge-1\)
The vertex is where y=-1 so this is the lowest value that y can take.
and here is the graph
https://www.desmos.com/calculator/jypgvfhfex
Hopefully you can get a lot from this Hayley but if you have questions, make sure you ask :D
