Question

For the quadratic equation 2.6(x - 7)^2 + 16, find and explain the following:

a) Coordinates of the vertex:

(-7, 16)
(7, 16)
(0, 0)
(0, 16)

Answer 1

vertex = (7, 16 )

Step-by-step explanation:

the equation of a quadratic in vertex form is

y = a(x - h)² + k

(h, k ) are the coordinates of the vertex and a is a multiplier

given

6(x - 7)² + 16 ← in vertex form , then

vertex = (h, k ) = (7, 16 )

Answer 2

To find the vertex's coordinates for the quadratic equation 2.6(x - 7)^2 + 16, we use the general vertex form a(x - h)^2 + k of a parabola. The vertex of the parabola represented by this equation is at (7, 16), which coincides with the variables h and k in the vertex form.

Step-by-step explanation:

The question asks to find the coordinates of the vertex for the quadratic equation 2.6(x - 7)^2 + 16. This is a vertex form of a quadratic equation, where the general form is a(x - h)^2 + k. Here, a is the coefficient that affects the width and direction of the parabola, while (h, k) are the coordinates of the vertex.

For the given equation, a = 2.6, h = 7, and k = 16. This directly gives us the coordinates of the vertex as (7, 16), because the vertex form shows that the graph of the quadratic equation is a parabola that opens upwards or downwards with vertex at the point (h, k). Therefore, the correct answer is (7, 16).