Chapter 3.1 to 3.3 Flashcard SY2023

Front

What are the zeros of the polynomial y = (x - 5)(x + 2)^2 and their multiplicities?

Back

Zeros: x = 5 (multiplicity 1), x = -2 (multiplicity 2)

Front

How do you find a polynomial function of degree 3 with given zeros?

Back

To find a polynomial of degree 3 with zeros 3i and -2, use the fact that complex zeros come in conjugate pairs. The polynomial is P(x) = (x - 3i)(x + 3i)(x + 2) = x^3 + 2x^2 + 9x + 18.

Front

What is the vertex of the parabola given by the equation y = 3(x + 5)^2 - 4?

Back

The vertex is (-5, -4).

Front

How do you write the standard form equation of a parabola given its vertex and a point it passes through?

Back

Use the vertex form y = a(x - h)^2 + k, where (h, k) is the vertex. Substitute the vertex and the point to find 'a'.

Front

What is the vertex form equation of a parabola with vertex (-4, 2) and passing through (0, 0)?

Back

The vertex form is f(x) = a(x + 4)^2 + 2. Substitute (0, 0) to find 'a'.

Front

What is the significance of the multiplicity of a zero in a polynomial?

Back

The multiplicity of a zero indicates how many times that zero is repeated and affects the graph's behavior at that point.

Front

How do you convert a polynomial from factored form to standard form?

Back

Expand the factors and combine like terms to write the polynomial in standard form.

Front

What is the relationship between the degree of a polynomial and the number of zeros it can have?

Back

A polynomial of degree n can have at most n zeros, counting multiplicities.

Front

What is the vertex of a parabola in standard form y = ax^2 + bx + c?

Back

The vertex can be found using the formula (-b/(2a), f(-b/(2a))).

Front

How do you determine the direction of opening for a parabola given by y = ax^2 + bx + c?

Back

If 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.