Answer:
(1, 3)
Step-by-step explanation:
You are given the h coordinate of the vertex as 1, but in order to find the k coordinate, you have to complete the square on the parabola. The first few steps are as follows. Set the parabola equal to 0 so you can solve for the vertex. Separate the x terms from the constant by moving the constant to the other side of the equals sign. The coefficient HAS to be a +1 (ours is a -2 so we have to factor it out). Let's start there. The first 2 steps result in this polynomial:
. Now we factor out the -2:
. Now we complete the square. This process is to take half the linear term, square it, and add it to both sides. Our linear term is 2x. Half of 2 is 1, and 1 squared is 1. We add 1 into the set of parenthesis. But we actually added into the parenthesis is +1(-2). The -2 out front is a multiplier and we cannot ignore it. Adding in to both sides looks like this:
. Simplifying gives us this:
On the left we have created a perfect square binomial which reflects the h coordinate of the vertex. Stating this binomial and moving the -3 over by addition and setting the polynomial equal to y:
From this form,
you can determine the coordinates of the vertex to be (1, 3)
"Adjacent" means next to each other. "Perpendicular" means at an angle of 90 degrees.
<span>Rectangles (this includes squares) have adjacent perpendicular sides. So do right triangles.</span>
The answer would be 28 and 1/4.
Choice D is true. It is just another way to write the given function.
To confirm choices A through C, replace x as follows and do the math:
For A, let x = -3. Does it really yield -11?
For B, let x = 0. Does it really yield 5?
For C, let x = 1/2. Does it really yield 4?
Take it from here.
It would fall between 6 and 7.
