s=-4.9t²+245t+14.7
s=-4.9(t²-245/4.9t)+14.7
s=-4.9(t²-50t)+14.7
s=-4.9(t²-50+625-625)+14.7
s=-4.9(t²-50+625)+(-4.9)(-625)+14.7
s=-4.9(t-25)²+30625.5+14.17
s=-4.9(t-25)²+3077.2
as you can see on the process of the problem on the part that says...s=-4.9(t²-50+625-625)+14.7...the +625-625 on the next step are on different positions like...-4.9(t²-50+625)...and(-4.9)(-625)...i want to know why and why the negative 625 its multiplying by the negative 4.9 please if somebody can explain me all this problem
the line
.....s=-4.9(t²-50+625-625)+14.7 ......
has a typo, should have been
s=-4.9(t²-50t+625-625)+14.7 , look at the bold part in the next line
s=-4.9(t²-50t+625-625)+14.7
s=-4.9[(t-25)²-625)]+14.7 , now the -4.9 has to be multiplied by both terms inside the square bracket
s = -4.9(t-25)² - 4.9(-625) + 14.7
s = -4.9(t-25)² + 3077.2
In the process provided, we are attempting to rewrite the given quadratic equation in the form of s = a(t - h)^2 + k, which represents the vertex form of a parabolic equation. This allows us to identify the vertex (h, k) and various characteristics of the parabola.
Let's break down the steps:
1. Starting with the given equation: s = -4.9t² + 245t + 14.7
2. To complete the square, we rewrite the equation as follows: s = -4.9(t² - 50t) + 14.7
- The purpose of this step is to group the terms involving t together.
- By factoring out -4.9 from the first two terms, we leave t² - 50t inside the parentheses.
3. Next, we add and subtract (625) inside the parentheses: s = -4.9(t² - 50t + 625 - 625) + 14.7
- The purpose is to create a perfect square trinomial, which can be factored later.
- By adding and subtracting 625 within the parentheses, we are not altering the equation, just rearranging it.
4. We then rewrite the equation as: s = -4.9[(t² - 50t + 625)] + (-4.9)(-625) + 14.7
- Since -4.9 is being factored out, the terms within the parentheses can be grouped together.
- (-4.9)(-625) is added separately to account for the operation outside of the parentheses.
5. Simplifying further, we have: s = -4.9(t - 25)² + 30625 + 14.7
- The trinomial t² - 50t + 625 can be factored as (t - 25)².
- The result of (-4.9)(-625) is 30625, and when added to 14.7, it becomes 30639.7.
6. Finally, the equation is further simplified to: s = -4.9(t - 25)² + 3077.2
- By adding 30639.7 to 14.7, it becomes 30654.4, which is rounded to 3077.2.
In conclusion, the purpose of the step involving (+625 - 625) is to rearrange the equation without changing its meaning. The multiplication of (-4.9)(-625) is performed to include the appropriate value back into the equation after factoring out -4.9. This process allows us to rewrite the equation in vertex form and better understand the characteristics of the parabolic equation.