16Hit1600
Advanced MathVery hardLeading coefficient from a vertex and a point

Advanced Math practice question

In the xy-plane, the parabola y = ax² + bx + c has its vertex at (3, −4) and passes through the point (1, 4). What is the value of a?

Answer: 2

In vertex form, y = a(x − 3)² − 4. Substituting (1, 4) gives 4 = 4a − 4, so a = 2.

Common wrong answers

If you answered 1
1 uses 4 = 4a without the −4.
If you answered 8
8 is 4a.
If you answered -2
−2 has the sign wrong; the parabola opens upward.

More Advanced Math questions

Not affiliated with the College Board. SAT is a trademark of the College Board.