Evaluate the expression
2
x
2
+
3
x
−
7
2x
2
+3x−7, when x=3

What are the steps

To evaluate the expression \(2x^2 + 3x - 7\) when \(x = 3\), follow these steps:

### Step 1: Substitute the value of \(x\) into the expression
Replace \(x\) with \(3\) in the expression:
\[
2(3)^2 + 3(3) - 7
\]

### Step 2: Calculate the square of \(x\)
First, calculate \(3^2\):
\[
3^2 = 9
\]

### Step 3: Multiply by the coefficients
Next, multiply the squared value by 2 and \(3\) by the coefficient:
\[
2(9) + 3(3) - 7 = 18 + 9 - 7
\]

### Step 4: Simplify the expression
Add and subtract the numbers:
\[
18 + 9 = 27
\]
\[
27 - 7 = 20
\]

### Final Answer:
So, the value of the expression when \(x = 3\) is \(20\).

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Do you want any more details or have any questions? 

Here are some related questions:

1. What is the expression's value when \(x = -3\)?
2. How would the expression change if the coefficient of \(x^2\) were doubled?
3. What happens if the constant term in the expression is changed to \( -10\)?
4. Can you graph the expression \(2x^2 + 3x - 7\)?
5. What are the roots of the expression \(2x^2 + 3x - 7\)?
6. How would you factorize the expression \(2x^2 + 3x - 7\)?
7. What is the vertex form of the expression \(2x^2 + 3x - 7\)?
8. How does the expression compare to \(x^2 + 3x - 7\) in terms of its graph?

**Tip**: When substituting values, ensure all steps are performed systematically to avoid mistakes in your calculations.

Learn how to evaluate the expression 2x^2 + 3x - 7 when x = 3 with a detailed step-by-step solution. Follow the substitution, coefficient multiplication, and simplification steps. Suitable for students in Grades 7-9.

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