Constructing a quadratic from zeros and a point
Use the zeros for the factors and a known point for the scale factor.
- Zeros
and give . - Substitute the known point to find
. - Keep the factorised form when it displays the zeros clearly.
Example 1
Find the scale factor
Find the quadratic function with the stated zeros and point. Zeros 1 and 4; passes through
Example 2
Find the quadratic function with the stated zeros and point. Zeros
Your turn
The zeros are 2 and 5. The graph passes through
Check answer
The zeros are -1 and 3. The graph passes through
Check answer
The zeros are -2 and 4. The graph passes through
Check answer
The zeros are 1 and 6. The graph passes through
Check answer
The zeros are -3 and -1. The graph passes through
Check answer
The zeros are 2 and 5. The graph passes through
The zeros are -1 and 3. The graph passes through
The zeros are -2 and 4. The graph passes through
The zeros are 1 and 6. The graph passes through
The zeros are -3 and -1. The graph passes through