1. **State the problem:** Find the x-intercepts of the function and solve the equation $3x^2 - 72 = 0$ using the square root property. 2. **Identify x-intercepts:** Given points $(-3,0)$ and $(5,0)$ are the x-intercepts where the function crosses the x-axis. 3. **Determine where the function is positive and negative:** The function is positive between $-3 < x < 5$ and negative when $x < -3$ or $x > 5$. 4. **Solve the equation $3x^2 - 72 = 0$ using the square root property:** Start by isolating the $x^2$ term: $$3x^2 - 72 = 0$$ $$3x^2 = 72$$ Divide both sides by 3: $$\cancel{3}x^2 = \cancel{3}24$$ $$x^2 = 24$$ Take the square root of both sides: $$x = \pm \sqrt{24}$$ Simplify the square root: $$x = \pm \sqrt{4 \times 6} = \pm 2\sqrt{6}$$ 5. **Final answer:** The solutions to the equation are $x = \pm 2\sqrt{6}$. This matches the x-intercepts approximately since $-3 \approx -2\sqrt{6}$ and $5 \approx 2\sqrt{6}$. The graph is a parabola opening upwards with x-intercepts at $-3$ and $5$, positive between these points, and negative outside this interval.