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Answer :
To find [tex]\( f(3) \)[/tex] for the function [tex]\( f(x) = -5x^2 - x + 20 \)[/tex], follow these steps:
1. Substitute [tex]\( x = 3 \)[/tex] into the function.
2. Calculate the expression [tex]\( -5 \times (3)^2 \)[/tex].
- First, square the 3: [tex]\( 3^2 = 9 \)[/tex].
- Then multiply by -5: [tex]\( -5 \times 9 = -45 \)[/tex].
3. Calculate the expression for the linear term: [tex]\( -x \)[/tex].
- Substitute [tex]\( x = 3 \)[/tex]: [tex]\( -3 \)[/tex].
4. Add the constant term 20 to these results.
5. Now put it all together:
- Start with [tex]\(-45\)[/tex] from the squared term.
- Add [tex]\(-3\)[/tex] from the linear term, giving [tex]\(-45 - 3 = -48\)[/tex].
- Finally, add 20: [tex]\(-48 + 20 = -28\)[/tex].
Therefore, [tex]\( f(3) = -28 \)[/tex].
1. Substitute [tex]\( x = 3 \)[/tex] into the function.
2. Calculate the expression [tex]\( -5 \times (3)^2 \)[/tex].
- First, square the 3: [tex]\( 3^2 = 9 \)[/tex].
- Then multiply by -5: [tex]\( -5 \times 9 = -45 \)[/tex].
3. Calculate the expression for the linear term: [tex]\( -x \)[/tex].
- Substitute [tex]\( x = 3 \)[/tex]: [tex]\( -3 \)[/tex].
4. Add the constant term 20 to these results.
5. Now put it all together:
- Start with [tex]\(-45\)[/tex] from the squared term.
- Add [tex]\(-3\)[/tex] from the linear term, giving [tex]\(-45 - 3 = -48\)[/tex].
- Finally, add 20: [tex]\(-48 + 20 = -28\)[/tex].
Therefore, [tex]\( f(3) = -28 \)[/tex].
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