Question

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

Your explanation should be at least 3 - 4 sentences and include at least 5 of the following words/phrase:
-squared term
-constant term
-quadratic function
-coefficient
-vertex form
-y variable

Answer 1

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

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)