Question

graph the equation $y = x^2 + 4x + 3$ on the accompanying set of axes. you must plot 5 points including the roots and the vertex. using the graph, determine the roots of the equation $x^2 + 4x + 3 = 0$.
click to plot points. click points to delete them.

Explanation:

Step1: Find roots (y=0)

Solve $x^2 + 4x + 3 = 0$. Factor: $(x+1)(x+3)=0$, so $x=-1, x=-3$. Points: $(-3,0), (-1,0)$.

Step2: Find vertex x-coordinate

Use $x=-\frac{b}{2a}$. For $a=1, b=4$: $x=-\frac{4}{2(1)}=-2$.

Step3: Find vertex y-coordinate

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

Step4: Find 2 extra points

Substitute $x=0$: $y=0+0+3=3$, point $(0,3)$.
Substitute $x=-4$: $y=(-4)^2+4(-4)+3=16-16+3=3$, point $(-4,3)$.

Step5: Identify roots from graph

Roots are x-values where $y=0$, which are the x-coordinates of the points where the parabola crosses the x-axis.

Answer:

The 5 points to plot are $(-4, 3)$, $(-3, 0)$, $(-2, -1)$, $(-1, 0)$, $(0, 3)$.
The roots of $x^2 + 4x + 3 = 0$ are $x=-3$ and $x=-1$.