Which is the graph of the function f(x) = one-halfx2 + 2x – 6?

on a coordinate plane, a parabola opens up. it goes through (negative 6, 0), has a vertex at (negative 2, negative 8), and goes through (2, 0).
on a coordinate plane, a parabola opens up. it goes through (negative 2, 0), has a vertex at (2, negative 8), and goes through (6, 0).
on a coordinate plane, a parabola opens up. it goes through (negative 4, 6), has a vertex at (4, negative 10), and goes through (8, negative 6).
on a coordinate plane, a parabola opens up. it goes through (negative 8, negative 6), has a vertex at (negative 4, negative 10), and goes through (4, 6).

On a coordinate plane, a parabola opens up. It goes through (negative 6, 0), has a vertex at (negative 2, negative 8), and goes through (2, 0)

Step-by-step explanation:

step 1

Find the vertex

we have

This is a vertical parabola open upward (because the leading coefficient is positive)

The vertex represent a minimum

Convert the equation in vertex form

Factor 1/2

Complete the square

Rewrite as perfect squares

The vertex is the point (-2,-8)

step 2

Find the x-intercepts

we know that

The x-intercepts are the values of x when the value of y is equal to zero

so

For f(x)=0

square root both sides

so

The x-intercepts are the points (-6,0) and (2,0)

therefore

On a coordinate plane, a parabola opens up. It goes through (negative 6, 0), has a vertex at (negative 2, negative 8), and goes through (2, 0)

the formula of a slope:

from a table we have

substitute:

the slope of f(x) is -1.

the graph of funcfion g(x) is a horizontal line. the slope of a horizontal line is equal 0. therefore the slope of g(x) is 0.

-1 < 0