Question

Graph the quadratic equation X^2+5x+6. Explain and locate where your roots are.

Answer 1

We have to graph the quadratic equation defined as:

$y=x^2+5x+6$

We can already identify that:

• The parabola opens upward (a > 0).

,

• The y-intercept is y = 6 (c = 6).

We can use the quadratic formula to find the roots:

$\begin{gathered} x=\frac{-5\pm\sqrt{5^2-4(1)(6)}}{2(1)} \\ x=\frac{-5\pm\sqrt{25-24}}{2} \\ x=\frac{-5\pm\sqrt{1}}{2} \\ \to x_1=\frac{-5-1}{2}=-\frac{6}{2}=-3 \\ \to x_2=\frac{-5+1}{2}=-\frac{4}{2}=-2 \end{gathered}$

The roots are x = -3 and x = -2.

We can graph the parabola with these 3 points as:

Answer: The roots are located at x = -3 and x= -2.