The graph of the function F(x) = 2x^2-8 is changed. The new graph can be represented by the function F(X)= -2x^2-4.

Which of the following describes the changes made to the graph of the
original function?

The graph now opens in the opposite direction. The y intercept is shifted up 4.

Step-by-step explanation:

F(x) = 2x^2-8

F(X)= -2x^2-4

We know that the graph is reflected over the y-intercept becuase of the negative sign in the second equation ( F(X)= -2x^2-4)

We know that the intercept is shifted up four, because the number decreased from 8 to 4, and the graph is reflected.

Attacthed is both of the equations graphed to help you visualize this shift!

step-by-step explanation:

my butt

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

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