For Exercises 1- 3: Match the function to the given graph by moving the sliders to set your \(a\), \(p\), \(q\) and \(r\) values. If you need to be more precise click on the slider and use your left and right arrows on your laptop.
Repeat by clicking on the "New Graph" button for questions 1-3.
Repeat by clicking on the "New Graph" button for questions 1-3.
For Exercises 4-7: Write the cubic function, in STANDARD FORM, whose graph is shown.
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8) Write the cubic function with x-intercepts \(x = 4\), multiplicity two, and \(x = -5\), multiplicity one, that passes through the point \((0,40)\). Leave in factored form.
9) Write the quartic function with x-intercepts \(x = -1\), multiplicity one, \(x = -3\), multiplicity one, and \(x = 3\), multiplicity two, that passes through the point \((0,-54)\). Leave in factored form.
10) Write the quartic function, in STANDARD FORM, whose graph is shown.
11) Write two DIFFERENT cubic functions that have x-intercepts at \((2, 0)\) and \((-3, 0)\). Explain how the graphs of these two equations differ.
12) Given the table of values answer the following questions:
a) Find the cubic regression model for the data.
b) Use your model to predict the value of \(y\) when \(x=20\).
13) Write a polynomial function, in STANDARD form, of least degree with rational coefficients that has \(-2\) and \(5i\) as zeros.
14) Write a polynomial function, in STANDARD form, of least degree with rational coefficients that has \(3\) and \(\sqrt{7}\) as zeros.
15) Write a polynomial function, in STANDARD form, of least degree with rational coefficients that has \(9\) and \(-2i\) as zeros.
16) Write a polynomial function, in STANDARD form, of least degree with rational coefficients that has \(-3\) and \(8+i\) as zeros.
17) Write a polynomial function, in STANDARD form, of least degree with rational coefficients that has \(2\) and \(6-3i\) as zeros.
Review
18) For the function \(g(x)=-\frac{1}{2}(x-2)^2(x+1)(x-4)^2\), identify the degree, leading coefficient, end behavior, and \(x\)- and \(y\)-intercepts. Then use this information to sketch a graph of the polynomial.
19) Given that \((2x+1)\) is a factor of \(f(x)=2x^3-7x^2-46x-21\), factor \(f(x)\) completely.
20) Given that \((x-5)\) is a factor of \(g(x)=x^4-3x^3-6x^2-12x-40\), find all zeros of \(g(x)\).
Solution Bank