is a quadratic function. 

One way to find the maximum or minimum value of a quadratic function such as   is to find the vertex of its parabola; its -coordinate will be the one extremum of the range. Whether it is the minimum or maximum value depends on the quadratic coefficient; since it is a positive value here (1), it will be a minimum value.

Set  and  equal to quadratic and linear coefficients 1 and 4, respectively, and evaluating the expression :

This gives the -coordinate of the vertex; the -coordinate, and the minimum value of , can be found by evaluating , which is done by substitution:

The range is therefore .

The -intercept of the graph of  is the point at which it intersects the -axis. Its -coordinate is 0; its -coordinate is , which can be found by substituting 0 for  in the definition:

,

the correct choice.

We know that right of the origin represents the positive x-direction, and above the origin represents the positive y-direction.  For Quadrant I, both the x-coordinate and y-coordinate must be positive, i.e. (+,+).  For quadrant II, the x-coordinate is negative, while the y-coordinate is positive, i.e. (+, -). For Quadrant III, both coordinates must be negative, i.e. (-, -).  For Quadrant IV, the x-coordinate is positive, and the y-coordinate is negative, i.e. (+, -).

By definition, quadrant I has positive coordinates, quadrant II has  coordinates, quadrant III has negative coordinates, and quadrant IV has  coordinates, as shown by the diagram below. Only one answer choice falls within quadrant II. All others lie in other coordinates or one of the axes.

- Quadrant II

- Quadrant I

- x-axis

- y-axis

- Quadrant III

To find out which quadrant a point lives in, we need to remember the qualities of each quadrant. By qualities, I mean the signs associated with the x and y values which are dependent on the quadrant the point resides in.

All coordinate pairs that are in Quadrant I will have a positive x value and a positive y value.

All coordinate pairs that are in Quadrant II will have a negative x value and a positive y value.

All coordinate pairs that are in Quadrant III will have a negative x value and a negative y value.

All coordinate pairs that are in Quadrant IV will have a positive x value and a negative y value.

For the point ,  we see that both the x and y coordinates are positive therefore, the point resides in Quadrant I. Another way to check, we can start from the origin and going right 4 units and up 3 units we will be in the upper-right section of the coordinate-plane, which is also known as Quadrant I.

Using the distance formula, calculate the distance from each of these points to the origin, (0, 0). While each answer choice has coordinates that add up to seven, (-1, 8) is the coordinate pair that produces the largest distance, namely , or approximately 8.06.

To get to , move right along the x-axis by , then move up on the y-axis by .

The sign in front of each number represents which direction to go on the x or y-axis starting at the origin . If the number is positive you go right on the x-axis or up on the y-axis. If the sign is negative then you move to the left on the x-axis or down on the y-axis.

The sign in front of each number represents which direction to go on the x or y-axis starting at the origin . If the number is positive you go right on the x-axis or up on the y-axis. If the sign is negative then you move to the left on the x-axis or down on the y-axis.

To get to , move left on the x-axis by , then move up on the y-axis by .

The sign in front of each number represents which direction to go on the x or y-axis starting at the origin . If the number is positive you go right on the x-axis or up on the y-axis. If the sign is negative then you move to the left on the x-axis or down on the y-axis.

To get to , only move up by  on the y-axis. Do not move along the x-axis because the x-coordinate is .

To get to , move right on the x-axis by  then move up on the y-axis by .

The sign in front of each number represents which direction to go on the x or y-axis starting at the origin . If the number is positive you go right on the x-axis or up on the y-axis. If the sign is negative then you move to the left on the x-axis or down on the y-axis.