Vertex Calculator
Find the vertex, axis of symmetry, and maximum or minimum value of a quadratic function. See the parabola and calculation steps instantly.
Quadratic equation
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x [-10, 10]
Graph settings
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Grid settings
Polar draws radial rings and 30° spokes. Type r = 4*sin(3*theta) to plot a polar curve.
X-axis settings
Y-axis settings
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Equal scaling keeps circles round. Independent scaling stretches each axis to fill the view.
Angle mode
Degrees: sin(90) = 1. Applies to graphs, roots, and intersections.
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What does this vertex tell you?
Calculation steps
Additional properties
What is a vertex?
The vertex is the turning point of a parabola: its lowest point when it opens upward, its highest when it opens downward. If a problem asks for the maximum or minimum value, the axis of symmetry, or the vertex form of an equation, start here and read the answer with its full working shown.
Explore vertex form
y = a(x - h)² + k
How coefficients change the vertex
Try a change to the current equation, then jump back at any time.
Vertex FAQ
What is the vertex of a parabola?
The vertex is the turning point of a parabola. It is the minimum point when the parabola opens upward and the maximum point when it opens downward.
How do you find the vertex of a quadratic equation?
For y = ax^2 + bx + c, calculate x = -b/(2a), then substitute that x-value into the equation to find y.
How do you find the axis of symmetry?
The axis of symmetry is the vertical line x = -b/(2a) passing through the vertex.
Can a vertex be a maximum or minimum?
Yes. If a > 0, the vertex is a minimum. If a < 0, it is a maximum.
How do you convert a quadratic equation to vertex form?
Find the vertex using h = -b / (2a) and k = f(h). Then express the equation as y = a(x - h)² + k.
Can a parabola have a vertex but no x-intercepts?
Yes. An upward-opening parabola whose vertex lies above the x-axis has no real x-intercepts. A downward-opening parabola whose vertex lies below the x-axis also has no real x-intercepts.