Question 1

Which of the following is the correct definition of a polynomial function?

Accepted Answer

A function of the form $$f(x) = a_n x^n + a_{n-1} x$$^{n-1}$$ + \ldots + a_1$ x + a_0$ where a_i$ are real numbers and a_n$$ 
eq 0$$

Question 2

What is the domain of any polynomial function?

Accepted Answer

All real numbers $$\mathbb{R}$$

Question 3

Given the polynomial $$f(x) = 4x^3$ - 5x^2$ + 7x - 2$$, what is the degree and the leading coefficient?

Accepted Answer

Degree: $$3$$, Leading coefficient: $$4$$

Question 4

According to the Fundamental Theorem of Algebra, how many roots does a polynomial of degree $$n$$ have over the complex numbers?

Accepted Answer

Exactly $$n$$ roots (counting multiplicities)

Question 5

Which of the following is NOT a polynomial function?

Accepted Answer

$$f(x) = \sqrt{x} + 2$$

Question 6

A quadratic function $$f(x) = ax^2$ + bx + c$$ has its vertex at $$x = -\frac{b}{2a}. If$$ $$a = 2$$ and $$b = -8$$, what is the $$x-$$coordinate of the vertex?

Accepted Answer

$$2$$

Question 7

Which method is best for solving the quadratic equation $$x^2 - 6x + 9 = 0$?

Accepted Answer

Factoring, because it is a perfect square trinomial

Question 8

If the discriminant $$D = b^2$ - 4ac of a $$quadratic equation is negative, what can be said about its solutions?

Accepted Answer

There are two unique complex solutions and no real solutions

Question 9

A quadratic function $$f(x) = -3x^2$ + 6x - 2$$ opens:

Accepted Answer

Downward, because the leading coefficient is negative

Question 10

Given the linear function $$f(x) = 5x - 3$$, what is the slope and $$y-$$intercept?

Accepted Answer

Slope: $$5$$, $$y-$$intercept: $$-3$$

Question 11

A real-world scenario: The height $$h (in $$meters) of a ball thrown upward is modeled by $$h(t) = -4.9t^2$ + 20t + 2. $$What is the maximum height reached by the ball?

Accepted Answer

$$22.04$$ meters

Question 12

Which of the following is the vertex form of a quadratic function?

Accepted Answer

$$f(x) = a(x - p)^2$ + q$$

Question 13

If a polynomial $$f(x)$$ has degree $$n$$, which statement is true about its range?

Accepted Answer

The range depends on whether $$n is $$even or odd

Question 14

Which of the following expressions is a quadratic function?

Accepted Answer

$$f(x) = 2x^2$ - 3x + 5$$

Question 15

A quadratic equation $$ax^2 + bx + c = 0$ has a discriminant D = 0$. What does this imply about its solutions?

Accepted Answer

There is one unique real solution (a repeated root)

Question 16

If $$f(x) = x^2$ - 4x + 7$$, what is the vertex of the parabola?

Accepted Answer

Vertex: $$(2, 3)$$

Question 17

Which of the following is a linear function?

Accepted Answer

$$f(x) = 6x + 1$$

Question 18

A quadratic function $$f(x) = ax^2$ + bx + c is $$concave up if:

Accepted Answer

$$a \u003e 0$$

Question 19

If a polynomial $$f(x)$$ has roots at $$x = 2$$ and $$x = -3$$, which of the following could be $$f(x)$$?

Accepted Answer

$$f(x) = (x - 2)(x + 3)$$

Polynomials and Quadratic Functions: Precalculus Study Notes

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