Question

The vertex of a parabola is at (-2,-3) when the x-value is -1, the y-value is -5 . What is the coefficient of the squared expression in the parabola's equation?

Answer 1

The coefficient of the square monomial within the equation of the parabola in standard form is -2.

Explanation:

The vertex form of the equation of the parabola is represented below:

`y - k = C\cdot (x-h)^(2)` (1)

Where:

`x` - Independent variable.

`y` - Dependent variable.

`h`,
`k` - Coordinates of the vertex.

`C` - Vertex parameter.

Please notice that vertex parameter is also the coefficient of the square monomial within the equation of the parabola in standard form. If we know that
`(h,k) = (-2,-3)` and
`(x,y) = (-1,-5)`, then the vertex parameter is:

`-5+3 = C\cdot (-1+2)^(2)`

`C = -2`

The coefficient of the square monomial within the equation of the parabola in standard form is -2.