Analyze the properties of quadratic functions and their graphical representations.
Functional Parameters
ConcavityOpens
Function Analysis
f(x) = 1x² + 0x + 0
Function Form
Vertex Coordinates(0.00, 0.00)
Axis of Symmetryx = 0.00
y-intercept0
x-intercepts0.00
Functional Range[0.00, ∞)
Function Visualizer
About this calculator
Quick Reference
Domain(-∞, ∞)
Vertex h-b / 2a
Vertex kf(h)
Understanding Quadratic Functions
A quadratic function is a second-degree polynomial function. Its graph is a curve called a parabola. These functions are uniquely defined by their vertex (the maximum or minimum point) and their concavity (whether they open up or down).
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Pro Tips
Vertex Form: f(x) = a(x - h)² + k, where (h, k) is the vertex.
Extreme Points: If a > 0, the vertex is the minimum. If a < 0, the vertex is the maximum.
Intercepts: The y-intercept is always (0, c). The x-intercepts are found by solving f(x) = 0.
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Fun Facts
"Parabolic reflectors are used in satellite dishes and car headlights because they focus waves to a single point."
"Golden Gate Bridge cables form a shape that is almost a parabola (technically a catenary, but very close)."
