91Ó°ÊÓ

Write the quadratic function in standard form and sketch its graph. Identify the vertex, axis of symmetry, and \(x\) -intercept(s). $$f(x)=x^{2}+8 x+13$$

Use a graphing utility to graph the quadratic function. Identify the vertex, axis of symmetry, and \(x\) -intercept(s). Then check your results algebraically by writing the quadratic function in standard form. $$f(x)=-\left(x^{2}+2 x-3\right)$$

Use a graphing utility to graph the quadratic function. Identify the vertex, axis of symmetry, and \(x\) -intercept(s). Then check your results algebraically by writing the quadratic function in standard form. $$f(x)=-\left(x^{2}+x-30\right)$$

(a) state the domains of \(f\) and \(g,\) (b) use a graphing utility to graph \(f\) and \(g\) in the same viewing window, and (c) explain why the graphing utility may not show the difference in the domains of \(f\) and \(g\). $$f(x)=\frac{x^{2}(x-2)}{x^{2}-2 x}, \quad g(x)=x$$

Write the standard form of the equation of the parabola that has the indicated vertex and passes through the given point. Vertex: (2,3)\(;\) point: (0,2)

Write the standard form of the equation of the parabola that has the indicated vertex and passes through the given point. $$\text { Vertex: }\left(-\frac{1}{4}, \frac{3}{2}\right) ; \text { point: }(-2,0)$$

Use a graphing utility to graph the quadratic function. Find the \(x\) -intercept(s) of the graph and compare them with the solutions of the corresponding quadratic equation when \(f(x)=0\) $$f(x)=-2 x^{2}+10 x$$

Use a graphing utility to graph the quadratic function. Find the \(x\) -intercept(s) of the graph and compare them with the solutions of the corresponding quadratic equation when \(f(x)=0\) $$f(x)=\frac{7}{10}\left(x^{2}+12 x-45\right)$$

find two quadratic functions, one that opens upward and one that opens downward, whose graphs have the given \(x\) -intercepts. (There are many correct answers.) $$(-1,0),(3,0)$$

Find the domain of the expression. Use a graphing utility to verify your result. $$\sqrt{\frac{x}{x^{2}-2 x-35}}$$