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

Step2: Find vertex y-value

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

Step3: Find x-intercepts

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

Step4: Find y-intercept

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

Step5: Plot & connect points

Plot vertex, intercepts, and symmetric points; draw parabola opening upward.

Answer:

Axis of symmetry: $x = -2$
Graph key points: Vertex $(-2, -1)$, x-intercepts $(-1, 0)$, $(-3, 0)$, y-intercept $(0, 3)$