example
Evaluate [latex]3{x}^{2}-9x+7[/latex] when
1. [latex]x=3[/latex]
2. [latex]x=-1[/latex]
Solution
| 1. [latex]x=3[/latex] |
|
|
[latex]3{x}^{2}-9x+7[/latex] |
| Substitute [latex]3[/latex] for [latex]x[/latex] |
[latex]3{\left(3\right)}^{2}-9\left(3\right)+7[/latex] |
| Simplify the expression with the exponent. |
[latex]3\cdot 9 - 9\left(3\right)+7[/latex] |
| Multiply. |
[latex]27 - 27+7[/latex] |
| Simplify. |
[latex]7[/latex] |
| 2. [latex]x=-1[/latex] |
|
|
[latex]3{x}^{2}-9x+7[/latex] |
| Substitute [latex]−1[/latex] for [latex]x[/latex] |
[latex]3{\left(-1\right)}^{2}-9\left(-1\right)+7[/latex] |
| Simplify the expression with the exponent. |
[latex]3\cdot 1 - 9\left(-1\right)+7[/latex] |
| Multiply. |
[latex]3+9+7[/latex] |
| Simplify. |
[latex]19[/latex] |
example
The polynomial [latex]-16{t}^{2}+300[/latex] gives the height of an object [latex]t[/latex] seconds after it is dropped from a [latex]300[/latex] foot tall bridge. Find the height after [latex]t=3[/latex] seconds.
Answer:
Solution
|
[latex]-16t^2+300[/latex] |
| Substitute [latex]3[/latex] for [latex]t[/latex] |
[latex]-16(\color{red}{3})^2+300[/latex] |
| Simplify the expression with the exponent. |
[latex]-16\cdot{9}+300[/latex] |
| Multiply. |
[latex]-144+300[/latex] |
| Simplify. |
[latex]156[/latex] |
