Question

Plot the x-intercept(s), y-intercept, vertex, and axis of symmetry for the function below.

Answer 1

g(x) = x^2 + 4x + 3

y-intercept:  let x=0.  Then y=3.  y-intercept is (0,3).

roots:  set g(x) = 0 and solve for x.  x=-1 and x=-3.

                                                                                       -4
axis of symmetry:  find x = -b / (2a), which here is x = ----- = -2
                                                                                        2

Answer 2

Given a quadratic equations:
g(x) = x² + 4x + 3

The equation cannot be factored as it's not a complete square.
therefore using the vertex form of a quadratic equation we will convert the equation into its vertex form and hence it's easy to graph a quadratic equation in vertex form.

The vertex for is :
g(x) = a(x - h)² + k 
where,
'h' is the axis of symmetry and (h,k) is the vertex.
So from the given equation we will rewrite the equation as:
x² + 4x + 3 = 0
x² + 4x = -3
x² + 4x + (2)² = -3 + (2)²
(x + 2)² = -3 + 4
(x + 2)² = 1
(x + 2)² - 1 = 0
Hence,
h = -2
and
k = -1

Thus our line of symmetry is x = -2 and vertex is (h,k) = (-2,-1)
Now,
we will find the x intercepts,
using the equation,
(x + 2)² = 1
square root on both sides,
√(x + 2)² = √1
x + 2 = ± 1
x = 1 - 2
x = -1
or
x = -1 -  2
x = -3

For y-intercept put x = 0 into the real equation:
g(x) = 0² + 4(0) + 3
y = 3