Answer:
x-intercepts: x =-1, x=-3 when y=0
y-intercept, y=3, when x =0
axis of symmetry x = -2
Step-by-step explanation:
We are given the function: [tex]g(x) = x^2+4x+3[/tex]
We need to draw the graph for
- x-intercept
- y-intercept
- axis of symmetry
of the given function.
For finding x-intercept put y=0, in the given function, we will put g(x) =0
We know that: g(x)=y
[tex]y=x^2+4x+3[/tex]
Putting y=0, we get:
[tex]0=x^2+4x+3[/tex]
Now, we need to solve the equation by factorization, to find value of x
[tex]0=x^2+4x+3\\We\:can\:write\\x^2+4x+3=0\\x^2+3x+x+3=0\\x(x+3)+1(x+3)=0\\(x+1)(x+3)=0\\x+1=0\:or\:x+3=0\\x=-1\:or\:x=-3[/tex]
So, we get x-intercepts: x =-1, x=-3 when y=0
For, finding y-intercept, put x =0
Putting x=0
[tex]g(x)=x^2+4x+3\\We\:know\:g(x)=y\\y=x^2+4x+3\\y=(0)^2+4(0)+3\\y=3[/tex]
So, we get y-intercept, y=3, when x =0
The formula used to calculate axis of symmetry is: [tex]x = \frac{-b}{2a}[/tex]
We have b=4 and a = 1
Putting values and finding axis of symmetry
[tex]x =-\frac{b}{2a} \\x=-\frac{4}{2(1)}\\x=-2[/tex]
So, we get axis of symmetry x = -2
We will also be requiring vertex of the function:
We can find h = -b/2a (same as axis of symmetry) we get h =-2
k can be found as k=f(h)
Put h=-2 in the function:
g(-2)=(-2)^2+4(-2)+3
g(-2)=4-8+3
g(-2)=-1
So, we get k = -1
The vertex (h,k) is (-2,-1)
Now, the graph is attached in figure below.
