Evaluate the expression y² - 5y + 7 when y = 3.
Understand the Problem
The question is asking to evaluate the quadratic expression y² - 5y + 7 by substituting y with the value 3.
Answer
The evaluated expression is $1$.
Answer for screen readers
The final result of the expression when $y = 3$ is $1$.
Steps to Solve
- Substituting y with 3
First, substitute the value of $y$ in the expression $y^2 - 5y + 7$: $$3^2 - 5(3) + 7$$
- Calculating $3^2$
Compute the square of 3: $$3^2 = 9$$
- Calculating $-5(3)$
Now, calculate $-5(3)$: $$-5(3) = -15$$
- Combining all parts
Now combine the calculated values into the expression: $$9 - 15 + 7$$
- Performing the arithmetic
First, calculate: $$9 - 15 = -6$$
Then, add 7: $$-6 + 7 = 1$$
The final result of the expression when $y = 3$ is $1$.
More Information
The quadratic expression evaluated gives you a numeric result based on the substituted value. This technique is often used to find specific outputs for mathematical models or equations.
Tips
- Forgetting to square the value of $y$ correctly.
- Confusing signs during arithmetic operations, especially with negative numbers.
- Skipping steps and making calculation errors by not writing down intermediate results.
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