What you’ll learn
Connect standard, vertex and factored forms.
Key idea
The binomial shift must reproduce the signed linear coefficient.
Equivalent polynomial forms match every coefficient; wrong inner sign reverses the linear term.
Worked example
Enter the exact value or ordered values in the format requested below.
Factored expression (x+7)(x-3) equals standard form x²+4x-21. Rewrite in complete vertex form (x-h)²+k.
- Expanding (x+7)(x-3) gives standard form x²+4x-21; add/subtract 4 to complete its square.
- Vertex form is (x+2)²-25; expanding it recovers the same linear coefficient 4 and constant -21, while roots are -7,3.
Answer: (x+2)²-25
Quick Check
Evaluate a worked attempt at connect standard, vertex and factored forms, identify the first invalid step, and provide the correction.
Convert x²+10x+21: Step 1 balances as x²+10x+25-4. Step 2 writes (x-5)²-4. Identify first invalid step and correct the vertex form.