Answer:
The output when x = -9 is f(x) = 187.
Step-by-step explanation:
We are given a function and asked to find the output of that function.
- The <u>input</u> of a function refers to a value that is substituted into the function in order to simplify it to a final value.
- The <u>output</u> of a function is the value that is achieved when the input is substituted into the equation and the function is evaluated.
Our standard function is in the form of a quadratic equation.
![ax^2+bx+c=0](https://tex.z-dn.net/?f=ax%5E2%2Bbx%2Bc%3D0)
Let's check for a change in the presentation of the first value in the equation.
![\bold{f(x)} = 2x^2 - 5x - 20\\\\\bold{f(-9)}](https://tex.z-dn.net/?f=%5Cbold%7Bf%28x%29%7D%20%3D%202x%5E2%20-%205x%20-%2020%5C%5C%5C%5C%5Cbold%7Bf%28-9%29%7D)
We see that x becomes -9. We also know that from conventional algebra, we need to make this change throughout the entire equation. Therefore, since we changed the x in f(x), we need to change it in 2x² - 5x - 20 as well.
![f(-9) = 2(-9)^2 - 5(-9) - 20](https://tex.z-dn.net/?f=f%28-9%29%20%3D%202%28-9%29%5E2%20-%205%28-9%29%20-%2020)
Now, it's time to simplify this function. Let's first simplify the first term of the function:
.
Let's follow PEMDAS in order to simplify the term.
P - Parentheses
E - Exponents
M - Multiplication
D - Division
A - Addition
S - Subtraction
When using this acronym, make sure that all operations are performed <u>left to right</u>.
We see that -9 is raised to the power of 2, so we square -9. Otherwise, we carry out the following operation.
![-9 \times -9 = 81](https://tex.z-dn.net/?f=-9%20%5Ctimes%20-9%20%3D%2081)
Then, we see that 2 is multiplied into this value. Therefore, we multiply 81 by 2.
![81 \times 2 = 162](https://tex.z-dn.net/?f=81%20%5Ctimes%202%20%3D%20162)
Now, we need to subtract the product of 5 and -9.
![5 \times -9 = -45](https://tex.z-dn.net/?f=5%20%5Ctimes%20-9%20%3D%20-45)
![162 - - 45 = 207](https://tex.z-dn.net/?f=162%20-%20-%2045%20%3D%20207)
Finally, we subtract 20 from this value.
![207 - 20 = 187](https://tex.z-dn.net/?f=207%20-%2020%20%3D%20187)
Therefore, the value of f(-9) is 187.