Advanced MathMediumLeading coefficient from the vertex and a point
Advanced Math practice question
A parabola in the xy-plane has its vertex at (2, 5) and passes through the point (3, 2). If its equation is written as y = a(x − 2)² + 5, what is the value of a?
Answer: -3 or −3
Substitute (3, 2): 2 = a(3 − 2)² + 5 = a + 5, so a = −3.
Common wrong answers
- If you answered 3
- 3 has the wrong sign; the parabola drops from 5 to 2 as x moves from 2 to 3, so a is negative.
- If you answered 7
- 7 adds 5 to 2 instead of subtracting.
- If you answered -1
- −1 would give y = 4 at x = 3, not 2.
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