Question

The vertex of this parabola is at (-5, 4). Which of the following could be its equation?

A. y = -(x + 5)2 + 4
B. y = -(x - 5)2 + 4
C. y = -(x + 5)2 - 4
D. y = -(x - 5)2 - 4

Answer 1

y = - (x+5)2 +4

Explanation:

Answer 2

Answer: The correct option is (A).
`y=-(x+5)^2+4.`

Step-by-step explanation: Given that the co-ordinates of the vertex of a parabola is (-5, 4).

We are to select the correct option that could be the equation of the given parabola.

We know that the standard equation of a [parabola with vertex (h, k) is given by

`y=a(x-h)^2+k~~~~~~~~~~~~~~~~~~~(i)`

Taking a = -1, equation (i) becomes

`y=-(x-h)^2+k.`

If the vertex is (h, k) = (-5, 4), then the equation of the parabola becomes

`y=-\{x-(-5)\}^2+4\\\\\Rightarrow y=-(x+5)^2+4.`

Therefore, if we take a = - 1, then
`y=-(x+5)^2+4.` could be the equation of the parabola.

Thus, (A) is the correct option.