Vertex From Standard Form

Vertex from Standard Form

A quadratic in standard form looks like y = ax² + bx + c. The vertex is the turning point of the parabola, and you can find it directly from the coefficients.

1) Find the x-coordinate

Use the coefficient of x and x²:

• x = -b / (2a)

This gives the horizontal position of the vertex.

2) Find the y-coordinate

Substitute that x-value back into the original equation:

• compute y = a(x²) + bx + c

The resulting point (x, y) is the vertex.

3) Simplify carefully

Reduce fractions, integers, and signs before writing the final answer. If the expression is exact, keep it exact rather than rounding.

4) Check your work

A quick check is to plug the vertex x-value into the equation again and confirm the y-value. If the parabola is supposed to open upward, the vertex should be a minimum; if it opens downward, it should be a maximum.

Common mistake to avoid

Do not confuse standard form with vertex form. In standard form, the vertex is not given directly—you must calculate it from a, b, and c.