<span>Given a quadratic equations:
g(x) = x</span>
²<span>
+ 4x + 3The 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)</span>
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 = -2and
k = -1Thus 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 = <span>± 1
x = 1 - 2
x = -1or
x = -1 - 2
x = -3
For y-intercept put x = 0 into the real equation:
</span>g(x) = 0² + 4(0) + 3
y = 3