1. **State the problem:** Solve for $a$ in the equation $$y = a(x - s)(x - t)$$ given $s = -5$, $t = -2$, and $y = -4$. 2. **Write the formula with given values:** Substitute $s$ and $t$ into the equation: $$y = a(x - (-5))(x - (-2)) = a(x + 5)(x + 2)$$ 3. **Choose a value for $x$ to solve for $a$:** Since $y$ is given as $-4$ but $x$ is not specified, we assume $x$ is a particular value where $y = -4$. To find $a$, we need a specific $x$ value. If $x$ is not given, we cannot solve for $a$ uniquely. However, if the problem implies $x$ is at the vertex or another point, we need that information. 4. **Assuming $x$ is a known value, for example $x = 0$:** Substitute $x=0$, $y=-4$, $s=-5$, $t=-2$: $$-4 = a(0 + 5)(0 + 2) = a(5)(2) = 10a$$ 5. **Solve for $a$:** $$a = \frac{-4}{10} = -\frac{2}{5}$$ 6. **Final answer:** $$a = -\frac{2}{5}$$ This means the value of $a$ that satisfies the equation at $x=0$ with the given $y$ is $-\frac{2}{5}$. If $x$ is different, substitute that $x$ value and solve similarly.