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

Answer:

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

Step-by-step 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.