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)
It will take Lauren 1.25 seconds to hit the water.
With the given information, we can write the following quadratic equation.
Now, just use the quadratic formula to solve the equation.
You will get 1.25 and -0.75 as the zeros of the equation (where Laruen hits the water).
Only 1.25 makes sense in the context of this problem.
Answer:
Draw a square and pentagon
Step-by-step explanation:
they are both polygons
$3.50×0.8=$2.80
$2.80×0.9=$2.52
The new price is $2.52
