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Similar Question 1
<p>Sketch <code class='latex inline'>f(x)</code>.</p><p><code class='latex inline'>g(x) = x^2 (x - 6)^3</code></p>
Similar Question 2
<p> Sketch the graph of polynomial function.</p><p><code class='latex inline'> \displaystyle P(x) = \frac{1}{64}x^3(x + 2)(x - 3)^2 </code></p>
Similar Question 3
<p>Sketch <code class='latex inline'>f(x)</code>.</p><p><code class='latex inline'>g(x) = x^2 (x - 6)^3</code></p>
Similar Questions
Learning Path
L1 Quick Intro to Factoring Trinomial with Leading a
L2 Introduction to Factoring ax^2+bx+c
L3 Factoring ax^2+bx+c, ex1
Now You Try
<p>Sketch <code class='latex inline'>f(x)</code>.</p><p><code class='latex inline'>g(x) = x^2 (x - 6)^3</code></p>
<p>Match each equation with the most suitable graph. Explain your reasoning.</p><p>(a) <code class='latex inline'>f(x) = 2(x + 1)^2(x - 3)</code></p><p>(b) <code class='latex inline'>g(x) = 2(x +1)^2(x - 3)^2</code></p><p>(c) <code class='latex inline'>p(x) = -2(x + 1)(x- 3)^2</code></p><p>(d) <code class='latex inline'>h(x) = x(x +1)(x -3)(x - 5)</code></p><img src="/qimages/160" />
<p>Find the cubic function that has the following zeros.</p><p>Zeros: <code class='latex inline'>-3, 0, 2</code></p>
<p>Graph <code class='latex inline'>f(x) = 3x^3 - 48x</code> showing:</p> <ul> <li>symmetry, if any</li> <li>x intercept, if any</li> <li>y intercept, if any</li> <li>asymptotes, if any</li> </ul>
<p>For each polynomial function:</p> <ul> <li>i) state the degree and the sign of the leading coefficient</li> <li>ii) describe the end behaviour of the graph of the function</li> <li>iii) determine the x-intercepts</li> </ul> <p><code class='latex inline'> \displaystyle p(x) = -(x + 5)^3(x -5)^3 </code></p>
<p>Square corners cut from a 30 cm by 20 cm piece of cardboard create a box when the 4 remaining tabs are folded upwards. The volume of the box is <code class='latex inline'> V(x) = x(30 - 2x) (20-2x)</code>, where x represents the height.</p><p>Calculate the volume of a box with a height of 2 cm.</p><p>Calculate the dimensions of a box with a volume of <code class='latex inline'>1000 cm^3</code></p><p>Solve <code class='latex inline'>V(x) > 0</code>, and discuss the meaning of your solution in the context of the question.</p><p>State the restrictions in the context of the question.</p>
<p>For the graph below</p> <ul> <li>State the sign of the leading coefficient. Justify your answer.</li> <li>Describe the end behaviour.</li> <li>Identify any symmetry.</li> <li>State the number of minimum and maximum points and local minimum and local maximum points. How are these related to the degree of the function?</li> </ul> <img src="/qimages/168" />
<p>Which of the choices represent a polynomial function that satisfies each set of conditions? </p><p>Degree <code class='latex inline'>4</code></p><p>Positive leading coefficient</p><p><code class='latex inline'>3</code> zeros</p><p><code class='latex inline'>3</code> turning points</p>
<p>For each polynomial function:</p> <ul> <li>i) state the degree and the sign of the leading coefficient</li> <li>ii) describe the end behaviour of the graph of the function</li> <li>iii) determine the x-intercepts</li> </ul> <p><code class='latex inline'> \displaystyle f(x) = (x - 4)(x + 3)(2x - 1) </code></p>
<p>Find the cubic function that has the following zeros.</p><p>Zeros: <code class='latex inline'>-2</code>, <code class='latex inline'>\frac{3}{4}</code>, <code class='latex inline'>5</code> (order 2)</p>
<p>Determine an equation for the polynomial function that corresponds to each graph.</p><img src="/qimages/301" />
<p>For each polynomial function:</p> <ul> <li>i) state the degree and the sign of the leading coefficient</li> <li>ii) describe the end behaviour of the graph of the function</li> <li>iii) determine the x-intercepts</li> </ul> <p><code class='latex inline'> \displaystyle g(x) = -2(x + 2)(x -2)(1+x)(x -1) </code></p>
<p>Find the cubic function that has the following zeros.</p><p>Zeros: -1 ,4 (order 2)</p>
<p>Sketch <code class='latex inline'>f(x)</code>.</p><p><code class='latex inline'>f(x) = -(x - 4)(x -1)(x + 5)</code></p>
<p>Sketch <code class='latex inline'>f(x)</code>.</p><p><code class='latex inline'>y = (x +1)^3</code></p>
<p>Graph the polynomial and determine how many local maxima and minima it has.</p><p><code class='latex inline'> \displaystyle y = (x + 2)^2(x - 2)^3 </code></p>
<p>Sketch <code class='latex inline'>f(x)</code>.</p><p><code class='latex inline'>y = x(2x +1)(x -3)(x -5)</code></p>
<p>Sketch the graph of polynomial function.</p><p><code class='latex inline'> \displaystyle P(x) = -\frac{1}{12}(x + 2)^2(x - 3)^3 </code></p>
<p>Sketch the graph of each function by getting into the factored form.</p><p><code class='latex inline'>y = x^3 - 9x^2 + 27x -27</code></p>
<p>Find the cubic function that has the following zeros.</p><p>Zeros: <code class='latex inline'>-2</code> (order 2), <code class='latex inline'>3</code> (order 2)</p>
<p>For the graph below</p> <ul> <li>State the sign of the leading coefficient. Justify your answer.</li> <li>Describe the end behaviour.</li> <li>Identify any symmetry.</li> <li>State the number of minimum and maximum points and local minimum and local maximum points. How are these related to the degree of the function?</li> </ul> <img src="/qimages/169" />
<p>Graph the function.</p><p><code class='latex inline'>\displaystyle g(x)=4(x+1)(x+2)(x-1) </code></p>
<p>Graph <code class='latex inline'>f(x) = x^4+4x^3+4x^2</code> showing:</p> <ul> <li>symmetry, if any</li> <li>x intercept, if any</li> <li>y intercept, if any</li> </ul>
<p>Find the cubic function that has the following zeros.</p><p>Zeros: -2 (order 3)</p>
<p> Sketch the graph of polynomial function.</p><p><code class='latex inline'> \displaystyle P(x) = \frac{1}{32}(2x - 1)(x + 1)(x + 3) </code></p>
<p>Determine an equation for each polynomial function. State whether the function is even, odd, or nether. Sketch a graph of </p><p>a cubic function with zeros <code class='latex inline'>-2</code> (order 2) and <code class='latex inline'>3</code> and <code class='latex inline'>y</code>-intercept <code class='latex inline'>9</code></p>
<p>Determine the equation of the polynomial function from each graph.</p><img src="/qimages/145" />
<p>Organize the following functions into families.</p><p><code class='latex inline'>\displaystyle \begin{array}{ccccc} &A &y = 2(x - 3)(x + 5) &G &y =\frac{1}{2}(x -3)(x + 5)\\ &B &y = -1.8(x - 3)^2(x + 5) &H &y = -5(x + 8)(x)(x + 6)\\ &C &y = -x(x +6)^2(x + 8) &I &y = (x - 3)(x + 5)\\ &D &y = (x -3)^2(x + 5) &J &y = \frac{3}{5}(x +5)(x + 3)^2\\ &E &y = (x -3)^2(x + 5) &K &y = \frac{x(x + 6)(x + 8)}{4}\\ &F &y = x(x +6)^2(x + 8) &L &y = 2(x + 5)(x^2 + 6x + 9)\\ \end{array} </code></p>
<p>Determine the equation of the polynomial function from each graph.</p><img src="/qimages/146" />
<p>Sketch the graph.</p><p><code class='latex inline'>y = x(x- 3)^2</code></p>
<p>Sketch <code class='latex inline'>f(x)</code>.</p><p><code class='latex inline'>y = -(x -1)(x +2)(x -3)</code></p>
<p>Which of the choices represent a polynomial function that satisfies each set of conditions? </p><p>degree 3, negative leading coefficient, 1 zero, no turning points</p>
<p>Determine the quadratic function that has zeros at <code class='latex inline'>-3</code> and <code class='latex inline'>-5</code>, if <code class='latex inline'>f(7) =-720</code>.</p>
<p>Sketch <code class='latex inline'>f(x)</code>.</p><p><code class='latex inline'>y = x(x - 4)(x -1)</code></p>
<p> Sketch the graph of polynomial function.</p><p><code class='latex inline'> \displaystyle P(x) = \frac{1}{64}x^3(x + 2)(x - 3)^2 </code></p>
<p>Polynomial function has zeros at <code class='latex inline'>-3, -1, 2</code>. Write an equation for each function. Then, sketch a graph of the function.</p><p>a quintic function that extends from quadrant <code class='latex inline'>3</code> to quadrant <code class='latex inline'>1</code></p>
<p>Graph the polynomial and determine how many local maxima and minima it has.</p><p>`\$ \displaystyle y = x(x + 1)(x -3)^2</p>
<p>Graph the function.</p><p><code class='latex inline'>\displaystyle f(x)=(x+2)^{2}(x+4)^{2} </code></p>
<p>Which of the choices represent a polynomial function that satisfies each set of conditions? </p><p>degree 4, negative leading coefficient, 2 zeros, 1 turning point</p>
<p>Sketch the graph of each function by getting in to the factored form.</p><p><code class='latex inline'>y = x^4 + 4x^3 +4x^2</code></p>
<p>For the function <code class='latex inline'>f(x) = 2(x - 3)^3(2x -1)^2(3x + 2)</code>, determine :</p><p>a.the degree of the function</p><p>b. the value of the leading coefficient of the function</p><p>c. the zeros and their orders</p><p>d. y-intercept</p><p>e. Sketch the function on the grid.</p><p>f. State the interval, in interval notation, where <code class='latex inline'>f(x) < 0</code></p>
<p>For the function <code class='latex inline'>\displaystyle f(x) = - \frac{1}{2}(4x^3 - 9x)(2 + x)^3(4-x)^2</code>, determine </p><p>a) the degree</p><p>b) the leading coefficient</p><p>c) the end behaviours </p><p>d) all zeros and their orders </p><p>e) Sketch</p><p>f) the interval, in interval notion, where <code class='latex inline'>f(x) \geq 0</code>.</p>
<p>Graph the polynomial and determine how many local maxima and minima it has.</p><p><code class='latex inline'> \displaystyle P(x) = x(x+ 1)^2(x + 2)^2(x + 3)^3 </code></p>
<p>Sketch <code class='latex inline'>f(x)</code>.</p><p><code class='latex inline'>y = x^2(3x -2)^2</code></p>
<p>Graph the polynomial and determine how many local maxima and minima it has.</p><p><code class='latex inline'> \displaystyle P(x) = -(x - 2)^3x^2(x + 5) </code></p>
<p>Sketch the graph of each function by getting in to the factored form.</p><p><code class='latex inline'>y = -x^4 - 15x^3 - 75x^2 - 125x</code></p>
<p>Graph the function.</p><p><code class='latex inline'>\displaystyle f(x)=(x-2)^{2}(x+1) </code></p>
<p>Graph the function.</p><p><code class='latex inline'>\displaystyle h(x)=(x+1)^{2}(x-1)(x-3) </code></p>
<p>Determine the cubic function that has zeros at <code class='latex inline'>-2</code>, <code class='latex inline'>3</code>, and <code class='latex inline'>4</code>, if <code class='latex inline'>f(5) = 28</code>.</p>
<p>Determine an equation for the polynomial function that corresponds to each graph.</p><img src="/qimages/304" />
<p>Sketch the graph of each function by getting in to the factored form.</p><p><code class='latex inline'>y = 3x^3 - 48 x</code></p>
<p>Each graph represents a polynomial function of degree 3, 4, 5, or 6. Determine the least possible degree of the function corresponding to each graph. Justify your answer.</p><img src="/qimages/170" />
<p>Find the cubic function that has the following zeros.</p><p>Zeros: <code class='latex inline'>3</code>, <code class='latex inline'>-\frac{1}{2}</code> (order 2)</p>
<p>For the graph below</p> <ul> <li>State the sign of the leading coefficient. Justify your answer.</li> <li>Describe the end behaviour.</li> <li>Identify any symmetry.</li> <li>State the number of minimum and maximum points and local minimum and local maximum points. How are these related to the degree of the function?</li> </ul> <img src="/qimages/167" />
<p>Sketch the graph of a polynomial function that satisfies each set of conditions.</p><p>degree 4, positive leading coefficient, 2 zeros, 3 turning points</p>
<p>The function <code class='latex inline'>f(x) = kx^3 - 8 x^2 - x + 3k + 1</code> has a zero when <code class='latex inline'>x = 2</code>. Determine the value of <code class='latex inline'>k</code>. </p>
<p>Determine an equation for the polynomial function that corresponds to each graph.</p><img src="/qimages/302" />
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