FLASHCARD#10 12th 1st period

Front

Match the graph to the function: f(x) = -x⁴-x³+5x²-6, f(x) = x⁴+3x²-3x+1, f(x) = -x³+2x²-x-6, f(x) = x⁴+x³+5x²-6

Back

The correct function is f(x) = x⁴+x³+5x²-6.

Front

What is the conjugate of 2 + √3?

Back

The conjugate is 2 - √3.

Front

Write the polynomial with the given zeros: 3i and -2.

Back

The polynomial is P(x) = x³ + 2x² + 9x + 18.

Front

What is the y-intercept of f(x) = -3x⁴ + x³ - 2x² + x - 1?

Back

The y-intercept is (0, -1).

Front

Define a polynomial function.

Back

A polynomial function is a function that can be expressed in the form f(x) = a_nx^n + a_(n-1)x^(n-1) + ... + a_1x + a_0, where a_n, a_(n-1), ..., a_0 are constants and n is a non-negative integer.

Front

What is a zero of a polynomial?

Back

A zero of a polynomial is a value of x for which the polynomial evaluates to zero.

Front

Explain the relationship between the degree of a polynomial and the number of zeros.

Back

The degree of a polynomial indicates the maximum number of zeros it can have, counting multiplicities.

Front

What is the significance of the leading coefficient in a polynomial?

Back

The leading coefficient determines the end behavior of the polynomial function.

Front

How do you find the y-intercept of a polynomial function?

Back

The y-intercept is found by evaluating the function at x = 0.

Front

What is the conjugate of a complex number?

Back

The conjugate of a complex number a + bi is a - bi.