General vertex form:
![y = m(x − a)² + b \: with \: vertex \: at \: (a, b)](https://tex.z-dn.net/?f=y%20%3D%20m%28x%20%E2%88%92%20a%29%C2%B2%20%2B%20b%20%20%5C%3A%20with%20%20%5C%3A%20vertex%20%5C%3A%20%20at%20%5C%3A%20%20%28a%2C%20b%29)
Given :
![y = 2x² + 5x - 3](https://tex.z-dn.net/?f=y%20%3D%202x%C2%B2%20%2B%205x%20%20-%203)
Extract "spread factor" m
![y = 2( x² + \frac{5}{2} x) - 3](https://tex.z-dn.net/?f=y%20%3D%202%28%20x%C2%B2%20%2B%20%20%5Cfrac%7B5%7D%7B2%7D%20x%29%20-%203)
Complete the square
![y = 2(x² + \frac{5}{2}x + ( \frac{5}{4})²) - 3](https://tex.z-dn.net/?f=y%20%3D%202%28x%C2%B2%20%20%2B%20%20%5Cfrac%7B5%7D%7B2%7Dx%20%2B%20%28%20%5Cfrac%7B5%7D%7B4%7D%29%C2%B2%29%20-%203)
![- 2( \frac{5}{4})²](https://tex.z-dn.net/?f=%20-%202%28%20%5Cfrac%7B5%7D%7B4%7D%29%C2%B2)
Write as a squared binomial and simplify the constant
![y = 2(x + \frac{5}{4})² - 6 \frac{1}{8}](https://tex.z-dn.net/?f=y%20%3D%202%28x%20%2B%20%20%5Cfrac%7B5%7D%7B4%7D%29%C2%B2%20-%206%20%5Cfrac%7B1%7D%7B8%7D%20)
Re-write to match signs of standard general form:
![y = 2(x - ( - \frac{5}{4}))² \: + ( - 6 \frac{1}{8})](https://tex.z-dn.net/?f=y%20%3D%202%28x%20-%20%28%20-%20%20%5Cfrac%7B5%7D%7B4%7D%29%29%C2%B2%20%5C%3A%20%20%2B%20%28%20-%206%20%5Cfrac%7B1%7D%7B8%7D%29)
Answer:
<h3>
14, 15, 16</h3>
Step-by-step explanation:
The consecutive integers iincrease by 1. So the middle integer of an odd number of consecutive integers is their mean. Three is an odd number of integers.
45:3 = 15 ← middle number
15 - 1 = 14 ← the smallest number
15 + 1 = 16 ← the largest number
Answer:
That's an isosceles right trapezoid. The legs equal hypotenuse * (1 / sq root (2))
legs = 7 * 1 / sqroot (2)
Answer is D
Step-by-step explanation: