Now You Try

<p>For the following, write the equations of three cubic functions that have the given zeros and belong to the same family of functions.</p><p>9, -5, -4</p>

<p>Sketch a graph of the functions with </p><p> <code class='latex inline'>(-2, 25)</code> and with zeros <code class='latex inline'>-\frac{5}{2}, -1, \frac{7}{2}</code>, and <code class='latex inline'>3</code>.</p>

<p>Determine an equation for the member of the family whose graph has y-intercept of 6 with zeros <code class='latex inline'>-2, -1</code>, and <code class='latex inline'>\frac{1}{2}</code>.</p>

<p>For the equation for a family of even functions with four x-intercepts, two of which are <code class='latex inline'>\frac{2}{3}</code> and 5.</p><p>What is the least degree this family of functors can have?</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 quartic function with zeros -2 (order 3) and 1 and y-intercept -2.</p>

<p>Determine an equation for the cubic function represented by this graph.</p><img src="/qimages/1641" />

<p>Write an equation for a family of polynomial functions with each set of zeros:</p><p><code class='latex inline'>-7, 0, 2, 5</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 quintic function with zeros -3, -2 (order 2). and 2 (order 2) that passes through the point (1.-18).</p>

<p>Sketch a graph of the functions whose</p><p>equation for the member of the family whose graph has <code class='latex inline'>y-</code>intercept of <code class='latex inline'>-4</code> and zeros <code class='latex inline'>-4, -1, 2</code>, and <code class='latex inline'>3</code>.</p>

<p>Determine an equation for the family of cubic functions with zeros <code class='latex inline'>-2, -1</code>, and <code class='latex inline'>\frac{1}{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 cubic function with a positive leading coefficient</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 quintic function with zeros -1(order 3) and 3 (order 2) that passes through the point (-2, 50).</p>

<p>For the following, write the equations of three quartic functions that have the given zeros and belong to the same family of functions.</p><p>4,-8, 1, 2</p>

<p>Write an equation for a family of polynomial functions with each set of zeros:</p><p><code class='latex inline'>-5, 2, 3</code></p>

<p>For the following, write the equations of three quartic functions that have the given zeros and belong to the same family of functions.</p><p>-6, 2, 5, 8</p>

<p>a) Determine an equation for the quartic function represented by this graph.</p><img src="/qimages/6953" /><p>b)
Use the graph to identify the intervals on which the function is below the x—axis.</p>

<p>Sketch a graph of a polynomial functions with </p><p> y-intercept of <code class='latex inline'>6</code> with zeros <code class='latex inline'>-2, -1</code>, and <code class='latex inline'>\frac{1}{2}</code>.</p>

<p>Write equations for two functions that belong to family with zeros <code class='latex inline'>-\frac{5}{2}, -1, \frac{7}{2}</code>, and <code class='latex inline'>3</code>.</p>

<p>Sketch the polynomials functions with </p><p> equations of polynomials with zeros <code class='latex inline'>-4, 0</code>, and <code class='latex inline'>2</code> and passing through <code class='latex inline'>(-2, 4)</code>.</p>

<p>Write equations for two functions that belong to this family with zeros <code class='latex inline'>-2, -1</code>, and <code class='latex inline'>\frac{1}{2}</code>.</p>

<p>Write an equation for a family of polynomial functions with each set of zeros:</p><p><code class='latex inline'>-4, -1, 9</code></p>

<p>For the equation for a family of even functions with four x-intercepts, two of which are <code class='latex inline'>\frac{2}{3}</code> and 5.</p><p>Determine an equation for the member of this family that passes through the point <code class='latex inline'>(-1, -96)</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 quartic function that touches the x-axis at <code class='latex inline'>-1</code>. <code class='latex inline'>-1</code> is a root of order 2</p>

<p>For the following, write the equations of three quartic functions that have the given zeros and belong to the same family of functions.</p><p>-7, 2, 3</p>

<p>For the following, write the equations of three cubic functions that have the given zeros and belong to the same family of functions.</p><p>5, -1, -2</p>

<p>Write an equation for a family of polynomial functions with each set of zeros:</p><p><code class='latex inline'>1, 6 ,-3</code></p>

<p>Determine a polynomial function P(x) that satisfies each set of conditions.</p><p><code class='latex inline'>P(-4) = P(-\frac{3}{4}) = P(\frac{1}{2}) = 0</code> and <code class='latex inline'>P(-2) = 50</code></p>

<p>Determine an equation for the family of cubic functions with zeros <code class='latex inline'>-4, 0</code>, and <code class='latex inline'>2</code>.</p>

<p>a) Determine an equation for the family of quartic functions with zeros <code class='latex inline'>-4, -1, 2</code>, and <code class='latex inline'>3</code>.</p><p>b) Write equations for two functions that belong to this family</p><p>c) Determine an equation for the member of the family whose graph has a y~intercept
of -4.</p><p>d) Sketch a graph of the functions in parts b) and c).</p>

<p>For the following, write the equations of three cubic functions that have the given zeros and belong to the same family of functions.</p><p><code class='latex inline'>-3, 6, 4</code></p>

<p>Determine the equation of the function with zeros at <code class='latex inline'>\pm 1</code> and <code class='latex inline'>-2</code>, and a y-intercept of <code class='latex inline'>-6</code>. Then sketch the function.</p>

<p>The zeros of a quartic function are <code class='latex inline'>-3, -1</code>, and <code class='latex inline'>2</code>(order 2). Determine</p><p>a) equations for two functions that satisfy this condition</p><p>b) an equation for a function that satisfies this condition and passes through the point (1, 4).</p>

<p>Write equations for two functors that belong to the family with zeros <code class='latex inline'>-4, -1, 2</code>, and <code class='latex inline'>3</code>.</p>

<p>Which quartic function has zeros at <code class='latex inline'>\displaystyle -2,0,1 </code>, and 3 , and satisfies <code class='latex inline'>\displaystyle f(2)=16 </code> ? a) <code class='latex inline'>\displaystyle f(x)=-2 x^{4}+4 x^{3}+10 x^{2}-12 x </code> b) <code class='latex inline'>\displaystyle f(x)=2 x^{4}-4 x^{3}-10 x^{2}+12 x </code> c) <code class='latex inline'>\displaystyle f(x)=2 x^{4}+4 x^{3}-10 x^{2}-12 x </code> d) <code class='latex inline'>\displaystyle f(x)=-2 x^{4}-4 x^{3}+10 x^{2}+12 x </code></p>

<p>Determine an equation for the family of cubic functions with zeros <code class='latex inline'>-\frac{5}{2}, -1, \frac{7}{2}</code>, and <code class='latex inline'>3</code>.</p>

<p>Determine an even function equation for a function with x-intercepts at <code class='latex inline'>\frac{2}{3}</code> and <code class='latex inline'>5</code>, passing through the point <code class='latex inline'>(-1, -96)</code></p>

<p>Write equations for two even functions with four x-intercepts, two of which are <code class='latex inline'>\frac{2}{3}</code> and 5.</p>

<p>For the following, write the equations of three quartic functions that have the given zeros and belong to the same family of functions.</p><p>-3, 3, -6, 6</p>

<p>Determine an equation for a function with <code class='latex inline'>x</code>-intercepts at <code class='latex inline'>\frac{2}{3}</code>, 5 and passing through the point <code class='latex inline'>(-1, -96)</code> and reflected on the <code class='latex inline'>x</code>-axis.</p>

<p>For the equation for a family of even functions with four x-intercepts, two of which are <code class='latex inline'>\frac{2}{3}</code> and 5.</p><p>Determine an equation for the member of this family that passes through the point <code class='latex inline'>(-1, -96)</code> and reflection in the x-axis.</p>

<p>Determine an equation for the polynomial function that corresponds to each graph.</p><img src="/qimages/303" />

<p>Determine a polynomial function P(x) that satisfies each set of conditions.</p><p><code class='latex inline'>P(3) = P(-1) = P(\frac{1}{2}) = P( -\frac{3}{2}) = 0</code> and <code class='latex inline'>P(1) = -18</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>A quartic function has zeros <code class='latex inline'>-1, 0</code>, and <code class='latex inline'>3</code> {order 2).</p><p>a) Write equations for two distinct functions that satisfy this description.</p><p>b) Determine an equation for a function satisfying this description that passes through the point <code class='latex inline'>(2, -18)</code>.</p><p>c) Sketch the function you found in part b). Then, determine the intervals on which the function is positive and the intervals on which it is negative.</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 quartic function that extends from quadrant <code class='latex inline'>3</code> to quadrant <code class='latex inline'>4</code></p>

<p>Write equations for two functions that belong to family of polynomials with zeros <code class='latex inline'>-4, 0</code>, and <code class='latex inline'>2</code>.</p>

<p>The zeros of quadratic function are <code class='latex inline'> -7</code> and <code class='latex inline'>-3</code>.</p><p><strong>(a)</strong> Determine an equation for the family of quadratic functions with these zeros.</p><p><strong>(b)</strong> Determine an equation for the member of the family that passes through the point <code class='latex inline'>(2, 18)</code>.</p>

<p>For the following, write the equations of three cubic functions that have the given zeros and belong to the same family of functions.</p><p>0, -1, 9, 10</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>Write an equation for a family of even functions with four x-intercepts, two of which are <code class='latex inline'>\frac{2}{3}</code> and <code class='latex inline'>5</code>.</p>

<p>Determine an equation for the member of the family whose graph passes through the point <code class='latex inline'>(-2, 25)</code> and with zeros <code class='latex inline'>-\frac{5}{2}, -1, \frac{7}{2}</code>, and <code class='latex inline'>3</code>.</p>

<p> Determine an equation for the member of the family whose graph which passes through <code class='latex inline'>(-2, 4)</code> with zeros <code class='latex inline'>-4, 0</code>, and <code class='latex inline'>2</code>.</p>

<p>Determine an equation for the member of the family whose graph has y-intercept of -4 and zeros -4, -1, 2, and 3.</p>