Question

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 expression in the parabola's equation?

Answer 1

The coefficient of the squared expression in the parabola's equation is 4.

Solution:

Given data:

Vertex of the parabola = (–5, –2), x = –4, y = 2

Vertex = (h, k)

Therefore, h = –5 and k = –2

Verex form of the parabola is $y=a(x-h)^2+k$ – – – – (1)

Substitute the value of x, y, h and k in equation in (1).

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

⇒ $2=a(-4+5)^2-2$

⇒ $2+2=a(1)^2$

⇒ $4=a$

Substitute a = 4 in equation (1), we get

$y=4(x-h)^2+k$

Hence the coefficient of the squared expression in the parabola's equation is 4.