Question

The vertex of this parabola is at (-5, -2). When the x-value is -4, they-value is 2. What is the coefficient of the squared expression in theparabola's equation?1010(-5,-2)-10O A1OB. 1C. 4.D. 5

Answer 1

As given by the question

There are given that the vertex of the parabola is, (-5, -2), x = -4, y = 2.

Now,

From the vertex,

`\begin{gathered} (h,\text{ k)=(-5, -2)} \\ h=-5 \\ k=-2 \end{gathered}`

vertex form of the parabola is:

`y=a(x-h)^2+k\ldots\text{ (1)}`

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

Then,

`\begin{gathered} y=a(x-h)^2+k \\ 2=a(-4-(-5))^2+(-2) \\ 2=a(-4+5)^2-2 \\ 2+2=a(1)^2 \\ a=4 \end{gathered}`

Then,

Substitute the value of a=4 into the equation (1)

`\begin{gathered} y=a(x-h)^2+k \\ y=4(x-h)^2+k \end{gathered}`

So,

The coefficient of the squared expression in the parabola equation is 4

Hence, the correct option is C.