Given f(x) = x² - 5x + 6, find f(3).
Understand the Problem
The question is asking to evaluate the function f(x) at x = 3, where the function is given as f(x) = x² - 5x + 6. This involves substituting 3 into the function and simplifying the expression.
Answer
$f(3) = 0$.
Answer for screen readers
The final answer is $f(3) = 0$.
Steps to Solve
- Substitute the value into the function
To find $f(3)$, substitute $x = 3$ into the function $f(x) = x^2 - 5x + 6$.
- Calculate the square of the value
Now calculate $3^2$: $$ 3^2 = 9 $$
- Calculate the product of the value and the coefficient
Next, calculate $-5 \cdot 3$: $$ -5 \cdot 3 = -15 $$
- Combine all parts of the function
Now combine the computed values: $$ f(3) = 9 - 15 + 6 $$
- Simplify the expression
Finally, simplify: $$ 9 - 15 + 6 = 0 $$
The final answer is $f(3) = 0$.
More Information
The function provided is a quadratic expression. By evaluating at specific points, we can determine the function's value, which in this case is 0 when evaluated at $x = 3$. This means that the point $(3, 0)$ lies on the graph of the function.
Tips
- Miscalculating the square of the number or the multiplication.
- Forgetting to combine all terms correctly at the end.
- Neglecting the sign in front of the exponent or multiplication.
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