91Ó°ÊÓ

Could a quadratic function have one real zero and one imaginary zero? Explain.

Complete the following. (a) Write the equation as \(a x^{2}+b x+c=0\) with \(a>0\) (b) Calculate the discriminant \(b^{2}-4 a c\) and determine the number of real solutions. (c) Solve the equation. $$ 3 x^{2}=12 $$

Two functions, \(f\) and \(g,\) are related by the given equation. Use the numerical representation of \(f\) to make a numerical representation of \(\mathbf{g}\). \(g(x)=f(-x)+1\) $$ \begin{array}{rrrrrr} x & -2 & -1 & 0 & 1 & 2 \\ f(x) & 11 & 8 & 5 & 2 & -1 \end{array} $$

Give an example of a quadratic function that has only real zeros and an example of one that has only imaginary zeros. How do their graphs compare? Explain how to determine from a graph whether a quadratic function has real zeros.

Complete the following. (a) Write the equation as \(a x^{2}+b x+c=0\) with \(a>0\) (b) Calculate the discriminant \(b^{2}-4 a c\) and determine the number of real solutions. (c) Solve the equation. $$ 8 x^{2}-2=14 $$

$$ \begin{array}{rrrrrr} x & -4 & -2 & 0 & 2 & 4 \\ \hline f(x) & 5 & 8 & 10 & 8 & 5 \end{array} $$

Complete the following. (a) Write the equation as \(a x^{2}+b x+c=0\) with \(a>0\) (b) Calculate the discriminant \(b^{2}-4 a c\) and determine the number of real solutions. (c) Solve the equation. $$ x^{2}-2 x=-1 $$

The points \((-12,6),(0,8),\) and \((8,-4)\) lie on the graph of \(y=f(x)\). Determine three points that lie on the graph of \(y=g(x)\). \(g(x)=f(x)+2\)

The points \((-12,6),(0,8),\) and \((8,-4)\) lie on the graph of \(y=f(x)\). Determine three points that lie on the graph of \(y=g(x)\). \(g(x)=f(x)-3\)

Complete the following. (a) Write the equation as \(a x^{2}+b x+c=0\) with \(a>0\) (b) Calculate the discriminant \(b^{2}-4 a c\) and determine the number of real solutions. (c) Solve the equation. $$ 6 x^{2}=4 x $$