Review for Test 2 Word AQ (1) PDF

## Question 1 of 35 Use the graph of the parabola to fill in the table. | | Answer | |---|---| | (a) Does the parabola open upward or downward? | downward | | (b) Find the coordinates of the vertex. | (-3, 1) | | (c) Find the intercept(s). | | | x-intercept(s): | -4, -2 | | y-intercept(s): | -...

## Question 1 of 35 Use the graph of the parabola to fill in the table. | | Answer | |---|---| | (a) Does the parabola open upward or downward? | downward | | (b) Find the coordinates of the vertex. | (-3, 1) | | (c) Find the intercept(s). | | | x-intercept(s): | -4, -2 | | y-intercept(s): | -8 | | (d) Find the equation of the axis of symmetry. | x=-3 | ## Question 2 of 35 Find all the zeros of the quadratic function. $y = x^2 + 8x + 16$ If there is more than one zero, separate them with commas. The zeros of the quadratic function are **x=-4**. ## Question 3 of 35 Write a quadratic function _h_ whose zeros are 5 and 4. The quadratic function is $y = (x-5)(x-4)$. ## Question 4 of 35 Find the _x_-intercept(s) and the coordinates of the vertex for the parabola $y = -x^2 - 4x + 12$. If there is more than one _x_-intercept, separate them with commas. The vertex is (-2, 16) and the _x_-intercepts are -6 and 2. ## Question 5 of 35 Rewrite the function $f(x) = -3(x + 2)^2 + 7$ in the form $f(x) = ax^2 + bx + c$. The function is $f(x) = -3x^2 - 12x - 5$. ## Question 6 of 35 Consider the following quadratic function: $g(x) = -3x^2 + 12x - 5$ (a) Write the equation in the form $g(x) = a(x - h)^2 + k$. Then give the vertex of its graph. The equation is $g(x) = -3(x-2)^2 + 7$ and the vertex is (2, 7). (b) Graph the function. The graph of the function is a parabola opening downward. ## Question 7 of 35 Answer the questions below about the quadratic function. $f(x) = 3x^2 - 12x + 16$ - Does the function have a minimum or maximum value? **minimum** - What is the function's minimum or maximum value? **y=4** - Where does the minimum or maximum value occur? **x=2** ## Question 8 of 35 A school wishes to form three sides of a rectangular playground using 280 meters of fencing. The playground borders the school building, so the fourth side does not need fencing. As shown below, one of the sides has length _x_ (in meters). (a) Find a function that gives the area _A(x)_ of the playground (in square meters) in terms of _x_. $A(x) = 280x - 2x^2$ (b) What side length _x_ gives the maximum area that the playground can have? **70 meters** (c) What is the maximum area that the playground can have? **9,800 square meters** ## Question 9 of 35 Find the equation of the quadratic function _g_ whose graph is shown below. The equation is $y = -2(x + 2)^2 + 5$. ## Question 10 of 35 Graph the solution to the following inequality on the number line. $(x+4)(x-7) ≥ 0$ The solution to the inequality is $x ≤ -4$ or $x ≥ 7$. ## Question 11 of 35 Graph the solution to the following inequality on the number line. $x^2 - 4x ≥ 0$ The solution is $x ≤ -4$ or $x ≥ 0$. ## Question 12 of 35 What are the leading coefficient and degree of the polynomial? $-10 + 18x^6 + 4x^3$ The leading coefficient is 18 and the degree is 6. ## Question 13 of 35 Consider the following polynomial functions: - $f(x) = (x-4)^2 (x^2 -4)$ - $g(x) = - 4x^4 + 12x^3$ Choose the graph of each function from the choices below. The graph of $f(x) = (x-4)^2 (x^2 -4)$ is Graph F and the graph of $g(x) = - 4x^4 + 12x^3$ is Graph C. ## Question 14 of 35 Choose the end behavior of the graph of each polynomial function. - $f(x) = -5x^3 + 4x^2 - 8x - 1$ - $f(x) = 2x^9 - x^5 + 2x^4 + 8$ - $f(x) = 4x(x-4)(x+2)$ - Function $f(x) = -5x^3 + 4x^2 - 8x - 1$ rises to the left and falls to the right. - Function $f(x) = 2x^9 - x^5 + 2x^4 + 8$ rises to the left and rises to the right. - Function $f(x) = 4x(x-4)(x+2)$ falls to the left and rises to the right. ## Question 15 of 35 Below is the graph of a polynomial function with real coefficients. All local extrema of the function are shown in the graph. - Over which intervals is the function increasing? **(-∞, -8), (-5, -2), (2, 5), (5, ∞)** - At which _x_-values does the function have local minima? **x = -8, -2, 5** - What is the sign of the function's leading coefficient? **Positive** - Which of the following is a possibility for the degree of the function? **6, 8** ## Question 16 of 35 Fill in the information about the parabolas below. - For each parabola, choose whether it opens upward or downward. | Parabola | Answer | |---|---| | $y = -\frac{2}{3} x^2$ | downward | | $y = -3x^2$ | downward | | $y = -\frac{1}{2} x^2$ | downward | | $y = -x^2$ | downward | - Choose the parabola with the narrowest graph. **$y = -3x^2$.** - Choose the parabola with the widest graph. **$y = -\frac{1}{2} x^2$.** ## Question 17 of 35 Find all real zeros of the function. $f(x) = -5x(x^2 - 16)(x^2 + 36)$ If there is more than one answer, separate them with commas. The zeros are **x = -4, 0, 4**. ## Question 18 of 35 Choose the end behavior of the graph of each polynomial function. - $f(x) = 2x^4 + 4x$ - $f(x) = 5x^3 - 4x^4 + 3x^2 + 2x$ - $f(x) = -3x(x+1)(x-4)^2$ - Function $f(x) = 2x^4 + 4x$ rises to the left and rises to the right. - Function $f(x) = 5x^3 - 4x^4 + 3x^2 + 2x$ falls to the left and falls to the right. - Function $f(x) = -3x(x+1)(x-4)^2$ falls to the left and falls to the right. ## Question 19 of 35 Suppose that the polynomial function _f_ is defined as follows. $f(x) = 6x(x-13)(x+2)^3$ List each zero of _f_ according to its multiplicity in the categories below. | Zero | Multiplicity | |---|---| | 0 | 1 | | 13 | 1 | | -2 | 3 | ## Question 20 of 35 Find a polynomial _f(x)_ of degree 4 that has the following zeros. -4, 2, 3, -5 Leave your answer in factored form. The polynomial is $f(x) =(x+4)(x-2)(x-3)(x+5)$. ## Question 21 of 35 Find all _y_-intercepts and _x_-intercepts of the graph of the function. $f(x) = 2x^3 + 2x^2 - 24x$ If there is more than one answer, separate them with commas. The _y_-intercept is (0, 0). The _x_-intercepts are (-4,0), (0,0) and (3,0). ## Question 22 of 35 Choose the end behavior of the graph of each polynomial function. - $f(x) = 6x^6 - 3x^4 - 4x^3 + 6x^2$ - $f(x) = 6x^3 - 3x^2 - 3x + 5x - 1$ - $f(x) = 2(x - 2)^2(x + 4)$ - Function $f(x) = 6x^6 - 3x^4 - 4x^3 + 6x^2$ rises to the left and rises to the right. - Function $f(x) = 6x^3 - 3x^2 - 3x + 5x - 1$ rises to the left and falls to the right. - Function $f(x) = 2(x - 2)^2(x + 4)$ rises to the left and rises to the right. ## Question 23 of 35 Divide. $(6x^3 + 9x^2 + 21x + 11) ÷ (3x^2 + 3x)$ The quotient is $2x + 1$ and the remainder is $18x + 11$. ## Question 24 of 35 Use synthetic division to find the quotient and remainder when $-4x^3 + 12x^2 + 18x - 14x + 24$ is divided by $x-4$ by completing the parts below. - Complete this synthetic division table. | | -4 | 12 | 18 | -14 | 24 | |---|---|---|---|---|---| | | | -16 | -16 | 8 | -24 | | | -4 | -4 | 2 | -6 | 0 | - Write your answer in the following form: Quotient + $\frac{Remainder}{x-4}$. The quotient is $-4x^3 + 4x^2 + 2x - 6$ and the remainder is 0. ## Question 25 of 35 Divide. $\frac{6x^2 + 11x}{2x}$ Simplify your answer as much as possible. The simplified answer is $3x + \frac{11}{2}$. ## Question 26 of 35 Use the remainder theorem to find P(2) for $P(x)=x^3-2x^2-4$. Specifically, give the quotient and the remainder for the associated division and the value of P(2). The quotient is $x^2 + 0x + 0$. This can be rewritten as $x^2$. The remainder is -4. P(2) = -4. ## Question 27 of 35 Use the rational zeros theorem to list all possible rational zeros of the following. $f(x) = 2x^4 - x^3 - x^2 - 3$ Be sure that no value in your list appears more than once. The possible rational zeros are $\pm 1, \pm 3, \pm \frac{1}{2}, \pm \frac{3}{2}, \pm \frac{1}{5}, \pm\frac{3}{5}$. ## Question 28 of 35 The function below has at least one rational zero. Use this fact to find all zeros of the function. $h(x) = 5x^3 + 4x^2 - 20x - 4$ If there is more than one zero, separate them with commas. Write exact values, not decimal approximations. The zeros are $-2, 2, -\frac{1}{5}$. ## Question 29 of 35 For the polynomial below, -2 is a zero. $f(x) = x^3 + 4x^2 + 3x - 2$ Express _f(x)_ as a product of linear factors. The polynomial is $f(x) = (x + 2)(x - (-1 + \sqrt{2}))(x-(-1-\sqrt{2}))$. ## Question 30 of 35 Graph all vertical and horizontal asymptotes of the rational function. $f(x) = \frac{9x-4}{3x-6}$ The vertical asymptote is $x = 2$. The horizontal asymptote is $y = 3$. ## Question 31 of 35 Graph all vertical and horizontal asymptotes of the rational function. $f(x) = \frac{2x^2 + 6x + 4}{-2x^2 + 5}$ The vertical asymptote is $x = -\frac{5}{2}$. There are no horizontal asymptotes. ## Question 32 of 35 Graph all asymptotes of the rational function. $f(x) = \frac{x^ 2 + x- 9}{x-2}$ The vertical asymptote is $x = 2$. There are no horizontal asymptotes, but a slant asymptote, $y = x + 3$. ## Question 33 of 35 The figure below shows the graph of a rational function _f_. It has vertical asymptotes $x = -4$ and $x= 6$, and horizontal asymptote $y = 0$. The graph has _x_-intercept 2, and it passes through the point (-1, 1). The equation for _f(x)_ has one of the five forms shown below. Choose the appropriate form for _f(x)_, and then write the equation. You can assume that _f(x)_ is in simplest form. The equation is $f(x) = \frac{-7(x-2)}{(x+4)(x-6)}$. ## Question 34 of 35 The graph of a rational function _f_ is shown below. Assume that all asymptotes and intercepts are shown and that the graph has no "holes". Use the graph to complete the following. - Find all _x_-intercepts and _y_-intercepts. **The _x_-intercept is -3 and the _y_-intercept is 0.** - Write the equations for all vertical and horizontal asymptotes. **The vertical asymptote is $x = -3$, and the horizontal asymptote is $y = 0$.** - Find the domain and range of _f_. **The domain is $(-∞,-3) ∪(-3, ∞)$ and the range is $(-∞, 0) ∪(0, ∞)$.** ## Question 35 of 35 The functions _f_ and _g_ are defined as follows. - $f(x) = \frac{x + 7}{x^2 + 12x + 35}$ - $g(x) = \frac{x^2}{x - 6}$ For each function, find the domain. Write each answer as an interval or union of intervals. The domain of $f(x) = \frac{x + 7}{x^2 + 12x + 35}$ is $(-∞, -7) ∪ (-7, -5) ∪(-5, ∞)$. The domain of $g(x) = \frac{x^2}{x - 6}$ is $( -∞, 6) ∪ ( 6, ∞)$.