Vertex Calculator
Find the vertex of any parabola instantly with step-by-step solutions
Calculate Vertex
Standard Form: y = ax² + bx + c
Vertex formula: h = -b/(2a), k = f(h)
Vertex:
Frequently Asked Questions
What is the vertex of a parabola?
The vertex is the highest or lowest point on a parabola. For upward-opening parabolas (a > 0), it's the minimum point. For downward-opening (a < 0), it's the maximum point. It's written as coordinates (h, k).
How do you find the vertex?
For y = ax² + bx + c, use h = -b/(2a) to find the x-coordinate, then substitute h into the equation to find k = f(h). The vertex is (h, k). This method works for any quadratic in standard form.
What is vertex form?
Vertex form is y = a(x - h)² + k, where (h, k) is the vertex. This form makes it easy to identify the vertex and graph the parabola. You can convert from standard form by completing the square.
What is the axis of symmetry?
The axis of symmetry is a vertical line that passes through the vertex, dividing the parabola into two mirror images. Its equation is x = h, where h is the x-coordinate of the vertex.
How does 'a' affect the vertex?
The value of 'a' doesn't change the vertex location, but it affects the parabola's shape. |a| > 1 makes it narrower, 0 < |a| < 1 makes it wider. If a > 0, parabola opens up; if a < 0, it opens down.
Can you find the vertex from factored form?
Yes! For y = a(x - p)(x - q), the x-coordinate of the vertex is h = (p + q)/2 (midpoint of the roots). Then substitute h into the equation to find k. Or expand to standard form first.