U3 Behavior of Polynomial Functions

Front

What is the effect of changing the constant 'c' in the quadratic equation y = ax² + bx + c?

Back

It affects the y-intercept of the parabola.

Front

What is the end behavior of the polynomial function y = -2x⁴ + 3x - 1?

Back

The end behavior is down-down.

Front

Which of the following is a possible equation for a polynomial function? 1) 2x⁴ - 3x³ + 7 = y 2) 1/3(4x + 3)(x - 2)(8x - 3) = y 3) -2(x + 1)(x - 2)(x - 3.5) = y 4) -x⁴ + x² - 6x + 7 = y

Back

1/3(4x + 3)(x - 2)(8x - 3) = y.

Front

Match the graph to the equation: y = (x - 1)²(x + 2)²

Back

This equation represents a polynomial with a double root at x = 1 and a double root at x = -2.

Front

What is the predicted end behavior of the polynomial function y = 4x⁵ + 7x?

Back

The end behavior is down-up.

Front

Define the term 'axis of symmetry' in relation to a parabola.

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves.

Front

What does the leading coefficient of a polynomial determine about its graph?

Back

The leading coefficient determines the direction in which the graph opens (upward or downward) and the end behavior.

Front

How do you find the x-coordinate of the vertex of a parabola given by y = ax² + bx + c?

Back

The x-coordinate of the vertex can be found using the formula x = -b/(2a).

Front

What is the significance of the degree of a polynomial function?

Back

The degree of a polynomial function indicates the highest power of the variable and determines the number of roots and the end behavior.

Front

Explain the term 'end behavior' in the context of polynomial functions.

Back

End behavior describes how the values of a polynomial function behave as x approaches positive or negative infinity.