Question

What are the coordinates of the vertex of a parabola whose equation is y+4=2(x−7)^2?

Answer 1

The coordinates of the vertex of the given parabola are (7, -4).

Step-by-step explanation:

The given equation is y+4=2(x−7)^2. To find the coordinates of the vertex of this parabola, we need to understand the standard form of a quadratic equation which is y = ax^2 + bx + c. By rearranging the given equation, we find that y = 2(x-7)^2 - 4. Comparing this equation with the standard form, we can see that the vertex form is y = a(x-h)^2 + k, where (h, k) represents the coordinates of the vertex. Therefore, the coordinates of the vertex of this parabola are (7, -4).

Answer 2

To find the vertex, the easiest way is to use vertex form; y= a(x - h)^2 + k where (h, k) is the vertex.

These are the steps to convert your equation to vertex form;

START: y+4 = 2(x - 7)^2
Subtract 4 from both sides: y = 2(x - 7)^2 - 4

The “h” and “k” are 7 and -4, respectively.

So... the vertex is (7, -4)

And there you have it! Your final answer is (7, -4)!

I recommend that you learn how to identify the different forms of equations!