Use the graphical method to solve the quadratic equation: $x^2 - 3x - 10 = 0$, where $-3 < x < 6$.

Steps to Solve

1. Create a table of values

To graph the equation $x^2 - 3x - 10 = 0$, we need to create a table of values for $x$ and $y$, where $y = x^2 - 3x - 10$. We are given that $-3 < x < 6$, so we'll choose integer values within this interval for $x$.

2. Calculate y-values

Now, we plug in the $x$ values into the equation $y = x^2 - 3x - 10$ to find the corresponding $y$ values.

For $x = -2$: $y = (-2)^2 - 3(-2) - 10 = 4 + 6 - 10 = 0$ For $x = -1$: $y = (-1)^2 - 3(-1) - 10 = 1 + 3 - 10 = -6$ For $x = 0$: $y = (0)^2 - 3(0) - 10 = 0 - 0 - 10 = -10$ For $x = 1$: $y = (1)^2 - 3(1) - 10 = 1 - 3 - 10 = -12$ For $x = 2$: $y = (2)^2 - 3(2) - 10 = 4 - 6 - 10 = -12$ For $x = 3$: $y = (3)^2 - 3(3) - 10 = 9 - 9 - 10 = -10$ For $x = 4$: $y = (4)^2 - 3(4) - 10 = 16 - 12 - 10 = -6$ For $x = 5$: $y = (5)^2 - 3(5) - 10 = 25 - 15 - 10 = 0$

3. Identify the x-intercepts

The solutions to the quadratic equation $x^2 - 3x - 10 = 0$ are the $x$-values where the graph intersects the $x$-axis (i.e., where $y = 0$). From our table, we see that $y = 0$ when $x = -2$ and $x = 5$.

4. Verify solutions within the given interval

Since $-3 < x < 6$, both $x = -2$ and $x = 5$ are within the specified interval.