Consider the function f(x)=15x^2+60-19 part a: write the function in vertex form. part b: name the vertex for the function

Part A) The function written in vertex form is

Part B) The vertex of the function is the point

Step-by-step explanation:

Part A) Write the function in vertex form

we know that

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

where

(h,k) is the vertex of the parabola

In this problem we have

Convert to vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

Factor the leading coefficient

Complete the square. Remember to balance the equation by adding the same constants to each side

Rewrite as perfect squares

-----> function in vertex form

Part B) Name the vertex for the function

we have

The vertex of the function is the point

The parabola open upward, so the vertex is a minimum

see the attached figure to better understand the problem

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