1. Read the Question Like a Detective
Ask: “What is the problem asking me to FIND?”
- Maximum height, area, revenue, etc.
- If the question asks for a maximum or minimum → it’s a quadratic.
2. Choose ONE thing to call “x”
Let x be _________.
Examples:
- number of seconds
- number of metres changed
- amount price increases
- width
3. Build Expressions From Words
Most quadratic problems come from multiplying two expressions.
AREA:
- width = x
- length = total – x
- area = x(total – x)
REVENUE:
- new price = starting price – x
- new number sold = starting amount + x
- revenue = (price)(amount)
PROJECTILES:
Use h(t) = at² + bt + c
4. Multiply at the End
Follow 3 lines:
1. Write what the question wants
2. Write both expressions
3. Multiply to make the quadratic
Example: A = x(20 – x) = 20x – x²
5. Use Vertex Formula for Maximum/Minimum
If equation is ax² + bx + c:
x = -b / (2a)
6. Safety Checklist
- Did I define x?
- Did I write expressions before multiplying?
- Did I create a quadratic?
- Did I use the vertex formula?
- Does the answer make sense?
7. Helpful Hints
- All quadratic word problems are area, projectiles, or money.
- Draw a picture.
- Label with x.
- Use a calculator.
8. Magic Words = Quadratic
- maximum/minimum
- thrown/dropped
- price changes
- width/length = x and (something – x)