Question

26 graph the function $f(x) = x^2 + 4x + 3$.
state the equation of the axis of symmetry of $f(x)$.

Explanation:

Step1: Find x-intercepts (set $f(x)=0$)

$x^2 + 4x + 3 = 0$
Factor: $(x+1)(x+3)=0$
Solutions: $x=-1, x=-3$

Step2: Find vertex (axis of symmetry)

Axis of symmetry formula: $x=-\frac{b}{2a}$
For $ax^2+bx+c$, $a=1, b=4$
$x=-\frac{4}{2(1)} = -2$

Step3: Find vertex y-value

Substitute $x=-2$ into $f(x)$:
$f(-2)=(-2)^2 + 4(-2) + 3 = 4 - 8 + 3 = -1$
Vertex: $(-2, -1)$

Step4: Find y-intercept (set $x=0$)

$f(0)=0^2 + 4(0) + 3 = 3$
Y-intercept: $(0, 3)$

Answer:

Equation of the axis of symmetry: $\boldsymbol{x=-2}$

(To graph the function: plot the x-intercepts $(-3,0)$ and $(-1,0)$, vertex $(-2,-1)$, y-intercept $(0,3)$, then draw a upward-opening parabola through these points.)