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)
Answer:
2x³ + x² - 11x - 15
Step-by-step explanation:
Step 1: Write out expression
2x³ + x² + 7x - 6 - (-2x + 10x + 10x + 9)
Step 2: Distribute negative
2x³ + x² + 7x - 6 + 2x - 10x - 10x - 9
Step 3: Combine like terms (x)
2x³ + x² + 9x - 10x - 10x - 9 - 6
2x³ + x² - x - 10x - 9 - 6
2x³ + x² - 11x - 9 - 6
Step 4: Combine like terms (constants)
2x³ + x² - 11x - 15
~Hello There!~

Rearrange for s

After 8 years, the new equation would be:

Cross multiply

Subtract 8

Substitute old equation

Solve to get m as 16.
s = 40.
Their current ages are 16 and 40 and the different is 24 years. Therefore, Caitlin is correct.
Hope This Helps You!
Good Luck :)
Have A Great Day ^_^
- Hannah ❤