Question

The vertex of this parabola is at (-2, -3). When the y-value is -2, the x-value is -5. What is the coefficient of the squared term in the parabola's equation?

Answer 1

The coefficient of the squared term in the parabola's equation, with the vertex at (-2, -3) and passing through the point (-5, -2), is found to be 1/9.

Step-by-step explanation:

To find the coefficient of the squared term in a parabola's equation, given the vertex and another point on the parabola, you can use the vertex form of a parabola's equation, which is:

y = a(x - h)^2 + k,

where (h, k) is the vertex of the parabola. In this case, the vertex is (-2, -3), so plugging that in:

y = a(x + 2)^2 - 3

We are also given the point (-5, -2), which lies on the parabola. Substituting these values into the equation, we get:

-2 = a(-5 + 2)^2 - 3

-2 = a(3)^2 - 3

-2 = 9a - 3

Add 3 to both sides:

-2 + 3 = 9a

1 = 9a

Divide both sides by 9:

a = 1/9

Therefore, the coefficient of the squared term in the parabola's equation is a = 1/9.