SAT Math: Finding the Vertex from Standard Form
29+ practice questions in Praczo
The concept, explained
- 1
For a quadratic in standard form y = ax² + bx + c, the x-coordinate of the vertex is x = -b / (2a).
- 2
To find the y-coordinate (the minimum or maximum value), plug the x-coordinate back into the equation.
- 3
If a > 0, the parabola opens upward (the vertex is a minimum). If a < 0, it opens downward (maximum).
- 4
This method is often much faster than completing the square, especially when the SAT only asks for the x-coordinate.
- 5
The axis of symmetry is the vertical line passing through the vertex: x = -b / (2a).
- ✗ Forgetting the negative sign in the formula (-b/2a).
- ✗ Thinking the x-coordinate is the minimum/maximum value itself (the y-coordinate is the actual value, x is just where it occurs).
SAT-style practice
At what value of x does the function f(x) = -2x² + 12x - 5 reach its maximum value?
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