Polynomial and Quadratic Functions flashcards

0/30

30 cards remaining

Take the chapter practice test

All 30 cards in this deckShow

In Quadratic Forms and Features, what does standard form mean?Quadratic Forms and Features: A quadratic sum form showing the constant term.
How do you locate its y-intercept?Quadratic Forms and Features: Set x=0 and evaluate the output.
In Quadratic Forms and Features, what does factored form mean?Quadratic Forms and Features: A product form exposing real zeros.
Why set y=0 to find intercepts?Quadratic Forms and Features: Every point on the x-axis has output zero.
In Quadratic Forms and Features, what does vertex form mean?Quadratic Forms and Features: A form exposing a quadratic turning point.
Why does the vertex occur at x=h?Quadratic Forms and Features: The squared factor is zero there.
In Transformations and Modeling with Quadratics, what does quadratic shift mean?Transformations and Modeling with Quadratics: The location changes in a transformed parabola.
Which coordinate does k control?Transformations and Modeling with Quadratics: The vertex output or vertical shift.
In Transformations and Modeling with Quadratics, what does feasible vertex mean?Transformations and Modeling with Quadratics: A vertex checked against practical input restrictions.
Why inspect domain endpoints?Transformations and Modeling with Quadratics: A restricted interval may place its optimum at an edge.
In Transformations and Modeling with Quadratics, what does units in a model mean?Transformations and Modeling with Quadratics: Interpreting coordinates and units in a quadratic application.
Can a negative elapsed time fit a launch model?Transformations and Modeling with Quadratics: Not when time starts at the launch event.
In Polynomial Functions and End Behavior, what does degree and leading term mean?Polynomial Functions and End Behavior: The highest nonzero exponent and its coefficient.
Why ignore lower terms in end behavior?Polynomial Functions and End Behavior: Their relative influence shrinks as |x| grows.
In Polynomial Functions and End Behavior, what does even and odd degree mean?Polynomial Functions and End Behavior: The parity pattern of polynomial end behavior.
Can lower-degree terms change the end directions?Polynomial Functions and End Behavior: No, the leading term controls them.
In Polynomial Functions and End Behavior, what does interpreting graphs mean?Polynomial Functions and End Behavior: Relating degree to possible graph features.
Can a degree-four polynomial have five distinct real zeros?Polynomial Functions and End Behavior: No, it has at most four distinct zeros.
In Zeros, Multiplicity, and Graph Shape, what does zeros as factors mean?Zeros, Multiplicity, and Graph Shape: The connection between polynomial zeros and factors.
How can a proposed zero be checked?Zeros, Multiplicity, and Graph Shape: Evaluate the polynomial at that input.
In Zeros, Multiplicity, and Graph Shape, what does even multiplicity mean?Zeros, Multiplicity, and Graph Shape: A repeated root whose exponent is even.
Does an even-multiplicity root necessarily cross?Zeros, Multiplicity, and Graph Shape: No, it generally touches and turns locally.
In Zeros, Multiplicity, and Graph Shape, what does odd multiplicity mean?Zeros, Multiplicity, and Graph Shape: A root repeated an odd number of times.
What does multiplicity count?Zeros, Multiplicity, and Graph Shape: The exponent on the associated linear factor.
In Building Polynomial Models, what does constructing from roots mean?Building Polynomial Models: A polynomial built from known intercepts.
Why is a scale factor k still needed?Building Polynomial Models: Roots alone do not fix every y-value.
In Building Polynomial Models, what does using a point mean?Building Polynomial Models: Calibrating a root-based polynomial model.
What if the point is itself a root?Building Polynomial Models: It may not determine the scale factor.
In Building Polynomial Models, what does checking a model mean?Building Polynomial Models: Evaluating a polynomial rule against context and data.
Why avoid distant extrapolation?Building Polynomial Models: The fitted behavior may not persist outside observed values.