Study guides › Level 8 · Algebra 2

How many times does a parabola cross the x-axis

Level 8 · Algebra 2 · for questions like “How many times does y = x² + 4x + 5 meet the x-axis?”

💡 The idea

The number b² − 4ac (the discriminant) decides:

• above 0: twice;
• exactly 0: once (it just touches);
• below 0: never.

✏️ Worked examples

1. y = x² + 4x + 5: 16 − 20 = −4, so never.

2. y = x² − 6x + 9: 36 − 36 = 0, so once.

3. y = x² + x − 6: 1 + 24 = 25, so twice.

⚠️ Watch out

• Minus a negative is a plus: with c = −6, −4ac = +24.

🎯 Try these

1. y = x² + 2x + 1
2. y = x² − 5x + 4
3. y = x² + 3x + 7

Answers: 1) once 2) twice 3) never

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