Question

Explain whether or not the following equation is a quadratic function in vertex form. y = 4(x - 2)^2 + 6.

Answer 1

Answer:

Yes, the following equation is a quadratic function in vertex form

Step-by-step explanation:

we know that

The quadratic function of the vertical parabola into vertex form is equal to

$y=a(x-h)^{2} +k$

where

(h,k) is the vertex of the parabola

If the coefficient a is > 0 ----> the parabola open upward (vertex is a minimum)

If the coefficient a is < 0 ----> the parabola open downward (vertex is a maximum)

in this problem we have

$y=4(x-2)^{2} +6$

The squared term contain the x-coordinate of the vertex

$h=2$

The constant term is the y-coordinate of the vertex

$k=6$

The vertex is the point (2,6)

The coefficient is equal to

$a=4$ ----> open upward (vertex is a minimum)