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.
Our standard function is in the form of a quadratic equation.
[tex]ax^2+bx+c=0[/tex]
Let's check for a change in the presentation of the first value in the equation.
[tex]\bold{f(x)} = 2x^2 - 5x - 20\\\\\bold{f(-9)}[/tex]
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.
[tex]f(-9) = 2(-9)^2 - 5(-9) - 20[/tex]
Now, it's time to simplify this function. Let's first simplify the first term of the function: [tex]2(-9)^2[/tex].
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 left to right.
We see that -9 is raised to the power of 2, so we square -9. Otherwise, we carry out the following operation.
[tex]-9 \times -9 = 81[/tex]
Then, we see that 2 is multiplied into this value. Therefore, we multiply 81 by 2.
[tex]81 \times 2 = 162[/tex]
Now, we need to subtract the product of 5 and -9.
[tex]5 \times -9 = -45[/tex]
[tex]162 - - 45 = 207[/tex]
Finally, we subtract 20 from this value.
[tex]207 - 20 = 187[/tex]
Therefore, the value of f(-9) is 187.
[tex] \sf f(x) = 2 {x}^{2} - 5x - 20[/tex]
[tex] \sf f( - 9)[/tex]
[tex] : \implies \sf f( - 9) = [2 \times( { - 9}^{2} )]-[ 5 \times - 9] - 20[/tex]
[tex] : \implies \sf f( - 9) = 2 \times 81 + 45 - 20[/tex]
[tex]: \implies \sf f( - 9) = 162 + 45 - 20[/tex]
[tex] : \implies \sf f( - 9) = 207 - 20[/tex]
[tex]: \implies \bf f( - 9) = 187[/tex]
