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 axis of symmetry

For $ax^2+bx+c$, axis is $x=-\frac{b}{2a}$.
Here $a=1, b=4$, so $x=-\frac{4}{2(1)}=-2$

Step2: Find vertex

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

Step3: Find x-intercepts

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

Step4: Find y-intercept

Set $x=0$:
$f(0)=0^2+4(0)+3=3$
Intercept: $(0,3)$

Step5: Find symmetric point

Point symmetric to $(0,3)$ over $x=-2$ is $(-4,3)$

Step6: Plot and connect points

Plot $(-3,0), (-2,-1), (-1,0), (0,3), (-4,3)$; draw upward-opening parabola.

Answer:

Axis of symmetry: $x = -2$
Key points for graph: $(-3,0), (-2,-1), (-1,0), (0,3), (-4,3)$