What are the x-intercepts of the function? b(x) = x^2 - 3x - 4

1. Understand x-intercepts: The x-intercepts of a function are the points where the graph of the function crosses the x-axis. At these points, the y-coordinate (or the function's value) is always 0. For a function $b(x)$, the x-intercepts occur when $b(x) = 0$.

1. Set the function to zero: Given the function $b(x) = x^2 - 3x - 4$, we need to find the values of $x$ for which $b(x) = 0$. So, we set up the equation: $$x^2 - 3x - 4 = 0$$ This is a quadratic equation.

3. Solve the quadratic equation: We can solve this quadratic equation by factoring, using the quadratic formula, or completing the square. Factoring is often the quickest method if possible.
We look for two numbers that multiply to -4 and add up to -3. These numbers are -4 and 1.
So, we can factor the equation as: $$(x - 4)(x + 1) = 0$$
4. Find the values of x: For the product of two factors to be zero, at least one of the factors must be zero. Therefore, we set each factor equal to zero and solve for $x$:
* $x - 4 = 0 \implies x = 4$
* $x + 1 = 0 \implies x = -1$

1. Write the x-intercepts as coordinates: The x-intercepts are the x-values where the function is zero. Since the y-coordinate is always 0 at the x-intercepts, the x-intercepts are the points $(-1, 0)$ and $(4, 0)$.