91Ó°ÊÓ

Determine whether the equation is linear in the variables \(x\) and \(y\). $$2 x-3 y=4$$

(a) determine the polynomial function whose graph passes through the given points, and (b) sketch the graph of the polynomial function, showing the given points. $$(2,4),(3,4),(4,4)$$

(a) determine the polynomial function whose graph passes through the given points, and (b) sketch the graph of the polynomial function, showing the given points. $$(-1,3),(0,0),(1,1),(4,58)$$

(a) determine the polynomial function whose graph passes through the given points, and (b) sketch the graph of the polynomial function, showing the given points. $$(2006,5),(2007,7),(2008,12)(z=x-2007)$$

(a) determine the polynomial function whose graph passes through the given points, and (b) sketch the graph of the polynomial function, showing the given points. $$\begin{array}{l} (2005,150),(2006,180),(2007,240),(2008,360) \\ (z=x-2005) \end{array}$$

The graph of a function \(f\) passes through the points \((0,1),\left(2, \frac{1}{3}\right)\) and \(\left(4, \frac{1}{5}\right)\). Find a quadratic function whose graph passes through these points.

The graph of a parabola passes through the points (0,1) and \(\left(\frac{1}{2}, \frac{1}{2}\right)\) and has a horizontal tangent at \(\left(\frac{1}{2}, \frac{1}{2}\right) .\) Find an equation for the parabola and sketch its graph.

The sales (in billions of dollars) for Wal-Mart stores from 2000 to 2007 are shown in the table. (Source: Wal-Mart) $$\begin{array}{l|llll} \hline \text {Year} & 2000 & 2001 & 2002 & 2003 \\ \text {Sales} & 191.3 & 217.8 & 244.5 & 256.3 \\ \hline \end{array}$$ $$\begin{array}{l|llll} \hline \text {Year} & 2004 & 2005 & 2006 & 2007 \\ \text {Sales} & 285.2 & 312.4 & 346.5 & 377.0 \\ \hline \end{array}$$ (a) Set up a system of equations to fit the data for the years \(2001,2003,2005,\) and 2007 to a cubic model. (b) Solve the system. Does the solution produce a reasonable model for predicting future sales? Explain

Find the solution set of the system of linear equations represented by the augmented matrix. $$\left[\begin{array}{rrrr} 1 & -1 & 0 & 3 \\ 0 & 1 & -2 & 1 \\ 0 & 0 & 1 & -1 \end{array}\right]$$

Prove that if a polynomial function \(p(x)=\) \(a_{0}+a_{1} x+a_{2} x^{2}\) is zero for \(x=-1, x=0,\) and \(x=1,\) then \(a_{0}=a_{1}=a_{2}=0\) Getting Started: Write a system of linear equations and solve the system for \(a_{0}, a_{1},\) and \(a_{2}\) (i) Substitute \(x=-1,0,\) and 1 into \(p(x)\) (ii) Set the result equal to 0 (iii) Solve the resulting system of linear equations in the variables \(a_{0}, a_{1},\) and \(a_{2}\)