What is the standard form of this function? f(x) = -(x − 4)2 + 2 a. f(x) = -x2 + 8x − 14 b. f(x) = x2 + 4x − 30 c. f(x) = -x2 + 4x − 30 d. f(x) = x2 + 8x − 14

option A. f(x) = -x² + 8x − 14

Step-by-step explanation:

The standard form of a quadratic equation in general is as following:

f(x) = ax² + bx + c.

Where a, b and c are constants and a ≠ 0.

So, for the given function:

f(x) = -(x − 4)² + 2

∴ f(x) = - (x-4) (x-4) + 2

∴ f(x) = - [ x(x-4) - 4(x-4) ] + 2

∴ f(x) = - ( x² - 4x -4x + 16 ) + 2

∴ f(x) = - ( x² - 8x + 16 ) + 2

∴ f(x) = -x² + 8x - 16 + 2

∴ f(x) = -x² + 8x - 14

So, the answer is option A. f(x) = -x² + 8x − 14

it is probably the graph on the bottom right.

when rotating a figure 180 degrees, imagine that you are able to take the figure and turn it clockwise or counterclockwise around a center point. to rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y). start by using a coordinate grid with coordinates for each vertex of the figure. the center point of the coordinate grid is located at (0, 0), which is what you will rotate the figure around. write down the original coordinates of the shape you are going to rotate. then, apply the rule. for example, coordinate (1, 2) becomes (-1, -2). another example would be, coordinate (-4, -2) becoming (4, 2). after you change each original coordinate to the rotated coordinate, you will draw your new figure.

step-by-step explanation: