Answer:
The coefficient of the squared term of the equation is 1/9.
Step-by-step explanation:
We are given that the vertex of the parabola is at (-2, -3). We also know that when the <em>y-</em>value is -2, the <em>x-</em>value is -5. Using this information we want to find the cofficient of the squared term in the parabola's equation.
Since we are given the vertex, we can use the vertex form:
Where <em>a</em> is the leading coefficient and (<em>h, k</em>) is the vertex.
Since the vertex is (-2, -3), <em>h</em> = -2 and <em>k</em> = -3:
Simplify:
We are also given that <em>y</em> = -2 when <em>x</em> = -5. Substitute:
Solve for <em>a</em>. Simplify:
Therefore, our full vertex equation is:
We can expand:
Simplify:
The coefficient of the squared term of the equation is 1/9.