Question

What is the function written in vertex form?

Answer 1

Answer:

The answer in the procedure

Step-by-step explanation:

The question does not present the graph, however it can be answered to help the student solve similar problems.

we know that

The equation of a vertical parabola into vertex form is equal to

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

where

a is a coefficient

(h,k) is the vertex

If the coefficient a is positive then the parabola open up and the vertex is a minimum

If the coefficient a is negative then the parabola open down and the vertex is a maximum

case A) we have

$f(x)=3(x+4)^{2}-6$

The vertex is the point (-4,-6)

a=3

therefore

The parabola open up, the vertex is a minimum

case B) we have

$f(x)=3(x+4)^{2}-38$

The vertex is the point (-4,-38)

a=3

therefore

The parabola open up, the vertex is a minimum

case C) we have

$f(x)=3(x-4)^{2}-6$

The vertex is the point (4,-6)

a=3

therefore

The parabola open up, the vertex is a minimum

case D) we have

$f(x)=3(x-4)^{2}-38$

The vertex is the point (4,-38)

a=3

therefore

The parabola open up, the vertex is a minimum