Advanced MathVery hardFinding the leading coefficient from the vertex and a point
Advanced Math practice question
The graph of a quadratic function in the xy-plane has its vertex at (2, 3) and passes through the point (4, 11). If the function is written as y = a(x − 2)² + 3, what is the value of a?
Answer: 2
Substitute the point (4, 11): 11 = a(4 − 2)² + 3, so 11 = 4a + 3, 4a = 8, a = 2.
Common wrong answers
- If you answered 1
- With a = 1 the point would give 1(4) + 3 = 7, not 11.
- If you answered 4
- 4 is (4 − 2)², the squared bracket, not a. Subtract 3 from 11 and divide by 4: a = 2.
- If you answered 8
- 8 is 11 − 3, the value of 4a. One more step: divide by 4.
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