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

Given:
vertex at (-2,-3), and a point on the parabola is (-5, -2)

The general formula for a parabola with vertex at (h,k) is given by
y=a(x-h)^2+k
in this problem, (h,k)=(-2,-3)
so
y=a(x+2)^2-3
We also know that one point on the parabola is (-5,-2), we will use this to solve for a.
-2=a(-5+2)^2-3
simplifying
-2=9a-3
solving for a
a=1/9
the complete equation of the parabola is therefore
y=(1/9)(x+2)^2-3

Check: at x=2, y=-3 => vertex
at x=-5, y=-2  => point on parabola.  so equation ok.

Answer 2

The coefficient of the squared term in the parabola's equation is -2.

What is Parabola ?

A parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped. It fits several superficially different mathematical descriptions, which can all be proved to define exactly the same curves.

Vertex form of a parabola: $y = a(x - h)^2 + k$, where (h, k) is the vertex of the parabola.

Plug in the vertex to get y = a(x + 2)² - 3. (The -2 got negated because of -h)

Plug in the point (-1,-5) to get -5 = a(-1+2)² -3 (This could be have been done in the previous step)

Now let's solve for a:

-5 = a(1)2-3

-5 = a-3

-2 = a

Thus, the coefficient of the squared term in the parabola's equation is -2.

Learn more about Parabola from:

https://brainly.com/question/4074088

#SPJ2