Area, consecutive integers and a ball thrown in the air all lead to a quadratic equation. Write it in standard form, factor it, then decide which answer fits the story.
The plan for every problem
Name the unknownLet a letter stand for what the question asks.
Write the equationTurn the words into math.
Get 0 on one sideStandard form: x² + bx + c = 0
FactorFind two numbers that multiply to c and add to b.
Set each factor to 0Each factor gives one answer.
Check the storyThrow out answers that make no sense, like a negative length.
Why you need 0 on one side
If two numbers multiply to 0, one of them must be 0. That only works with 0. If (w + 8)(w − 5) = 0, then w + 8 = 0 or w − 5 = 0. If the product were 40 instead, you couldn't say anything about either factor.
Worked examples
Your turn
Practice problemSolved: 0
1 · Get 0 on one side
2 · Factor
3 · Set each factor to 0
4 · Check the storyWhich answers make sense here? Select every one that fits, then check.
Question 1 of 5Score: 0
Common mistakes
Factoring before getting 0 on one side.w(w + 3) = 40 does not mean w = 40. Subtract 40 first, then factor.
Mixing up the signs. The two numbers must multiply to c and add to b. For c = −40, one number is negative.
Flipping the sign when solving.w + 8 = 0 gives w = −8, not 8.
Keeping an answer that can't happen. Lengths, times and "positive" numbers can't be negative. But sometimes both answers fit, like a ball passing the same height on the way up and on the way down.