The vertex of this parabola is at (-5,-2). When the x-value is -4, the y-value is 2. What is the coefficient of the squared term in the parabola equation?

llm

Answered on Mon Nov 20 2023

The coefficient of the squared term (a) in the parabola's equation of the form y = a(x - h)^2 + k,

The vertex is at the point (h, k), we can use the given vertex (-5,-2) and the point (-4,2) which lies on the parabola.

Since the vertex is (-5,-2), we know that h = -5 and k = -2.

Using the point (-4,2), we can plug these into the equation to find 'a'.

2 = a(-4 - (-5))^2 + (-2)

2 = a(-4 + 5)^2 - 2

2 = a(1)^2 - 2

2 = a - 2

4 = a

a = 4.

So the coefficient of the squared term in the parabola's equation is 4.