quadratic functions
U-shaped graph equations
A quadratic function is a polynomial function of degree two, producing a U-shaped curve called a parabola when graphed.
The standard form is ax² + bx + c, where a is nonzero.
Quadratic functions model trajectories, optimize areas, and appear throughout physics and economics: The ball's height follows a quadratic function of time.
Expression with variable terms
- equationMathematical equality assertion
- factorizationDecomposing into multiplicative parts
- discriminantFormula determining root nature
- rootsUnderground nutrient absorbers
coefficients · solutions · trinomial · variable · inequality · complex numbers · binomial · standard form
Tapering to apex
- focusConcentrated attention point
- directrixLine defining conic sections
- axis of symmetryLine dividing congruent halves
- graphingPlotting data visually
concavity · convexity · x-intercepts · y-intercept · zeros · curve · U-shape · focal length
Greatest permitted quantity
- minimumSmallest possible quantity
- turning pointDecisive moment of change
- axis of symmetryLine dividing congruent halves
- optimumMost favorable condition
critical point · extremum · peak · trough · transformation · stretch · compression · reflection
Parabolic path under gravity
- trajectoryPath of moving object
- optimizationMaximizing efficiency or performance
- profit maximizationPursuing greatest possible gains
- ball tossThrowing a sphere
satellite dish · water fountain · physics · engineering · architecture · ballistics
Two-axis graphing system
- x-axisGraph's horizontal reference line
- y-axisGraph's vertical reference
- originStarting point or source
- plottingDevising a secret plan
intercepts · symmetry · translation · dilation · transformation · domain · range · continuous
polynomial
Expression with variable terms
- equationMathematical equality assertion
- factorizationDecomposing into multiplicative parts
- discriminantFormula determining root nature
roots · coefficients · solutions · trinomial · variable · inequality · complex numbers · binomial · standard form · real roots
conic
Tapering to apex
- focusConcentrated attention point
- directrixLine defining conic sections
- axis of symmetryLine dividing congruent halves
graphing · concavity · convexity · x-intercepts · y-intercept · zeros · curve · U-shape · focal length · conic section
maximum
Greatest permitted quantity
- minimumSmallest possible quantity
- turning pointDecisive moment of change
- axis of symmetryLine dividing congruent halves
optimum · critical point · extremum · peak · trough · transformation · stretch · compression · reflection
projectile motion
Parabolic path under gravity
- trajectoryPath of moving object
- optimizationMaximizing efficiency or performance
- profit maximizationPursuing greatest possible gains
ball toss · satellite dish · water fountain · physics · engineering · architecture · ballistics
coordinate plane
Two-axis graphing system
- x-axisGraph's horizontal reference line
- y-axisGraph's vertical reference
- originStarting point or source
plotting · intercepts · symmetry · translation · dilation · transformation · domain · range · continuous · scale
quadratic functionslinear functions
Equations producing straight graphs
straight lines · linear equations · horizontal lines · vertical lines · lines
quadratic, quadrat, quadrature, quadrant, quad, square, squared, squaring, squares