Chapter 2

Find the average rate of change of each ficnetion on the given interval. $$f(x)=-2 x^{3} ; \text { interval: }[-2,0]$$

Find the vertex and axis of symmetry of the associated parabola for each quadratic function.Then find at least two additional points on the parabola and sketch the parabola by hand. $$f(x)=10 x^{2}-65$$

For what value(s) of \(a\) will the inequality \(a x^{2}<0\) have no real-valued solution? Explain.

Solve the radical equation to find all real solutions. Check your solutions. $$\sqrt{x+3}-\sqrt{x+2}=4$$

In Exercises \(41-48,\) use \(f\) and \(g\) given by the following tables of values. $$\begin{array}{ccccc}x & -1 & 0 & 3 & 6 \\\\\hline f(x) & -2 & 3 & 4 & 2\end{array}$$ $$\begin{array}{ccccc}x & -2 & 1 & 2 & 4 \\\\\hline g(x) & 0 & 6 & -2 & 3\end{array}$$ Is \((f \circ g)(2)\) defined? Why or why not?

Find \(x+y, x-y, x y,\) and \(x / y\). $$x=-2-i ; y=i+2$$

Solve the quadratic equation by using the quadratic formula. Find only real solutions. $$-3 x^{2}+2 x-1=0$$

Find the average rate of change of each ficnetion on the given interval. $$f(x)=2 x^{2}+3 x-1 ; \text { interval: }[-2,-1]$$

Find the vertex and axis of symmetry of the associated parabola for each quadratic function.Then find at least two additional points on the parabola and sketch the parabola by hand. $$f(t)=\frac{1}{3}-3 t+t^{2}$$

In Exercises \(49-66,\) let \(f(x)=x^{2}+x, g(x)=\sqrt{x},\) and \(h(x)=-3 x\) Evaluate each of the following. $$(f \circ h)(5)$$

Explain why \((x+1)^{2} \leq 0\) has a solution, whereas \((x+1)^{2}<0\) has no real-valued solution.

Solve the radical equation to find all real solutions. Check your solutions. $$\sqrt{x+3}+\sqrt{x-5}=4$$

Solve the quadratic equation by using the quadratic formula. Find only real solutions. $$-l^{2}+40 l=100$$

Find the average rate of change of each ficnetion on the given interval. $$f(x)=3 x^{3}+x^{2}+4 ; \text { interval: }[-2,0]$$

Find the vertex and axis of symmetry of the associated parabola for each quadratic function.Then find at least two additional points on the parabola and sketch the parabola by hand. $$h(t)=1-\frac{1}{2} t-t^{2}$$

In Exercises \(49-66,\) let \(f(x)=x^{2}+x, g(x)=\sqrt{x},\) and \(h(x)=-3 x\) Evaluate each of the following. $$(f \circ h)(1)$$

Give graphical and algebraic explanations of why \(x^{2}+1<-x\) has no real- valued solution.

Solve the radical equation to find all real solutions. Check your solutions. $$\sqrt{x+10}-\sqrt{x-1}=3$$

Solve the quadratic equation by using the quadratic formula. Find only real solutions. $$-x^{2}+50 x=300$$

Find the average rate of change of each ficnetion on the given interval. $$f(x)=-x^{4}+6 x^{2}-1 ; \text { interval: }[1,2]$$

Find the vertex and axis of symmetry of the associated parabola for each quadratic function. Sketch the parabola. Find the intervals on which the function is increasing and decreasing, and find the range. $$f(x)=-x^{2}+10 x-8$$

In Exercises \(49-66,\) let \(f(x)=x^{2}+x, g(x)=\sqrt{x},\) and \(h(x)=-3 x\) Evaluate each of the following. $$(f \circ h)(-2)$$

Solve the equation to find all real solutions. Check your solutions. $$x-4 \sqrt{x}=-3$$

Compute the zeros of the quadratic function. $$h(x)=-3 x^{2}-10$$

Solve the quadratic equation by using the quadratic formula. Find only real solutions. $$\frac{1}{2} t^{2}-4 t-3=0$$

Find the vertex and axis of symmetry of the associated parabola for each quadratic function. Sketch the parabola. Find the intervals on which the function is increasing and decreasing, and find the range. $$h(x)=x^{2}+6 x-7$$

In Exercises \(49-66,\) let \(f(x)=x^{2}+x, g(x)=\sqrt{x},\) and \(h(x)=-3 x\) Evaluate each of the following. $$(f \circ h)(-1)$$

Solve the equation to find all real solutions. Check your solutions. $$x-6 \sqrt{x}=-5$$

Compute the zeros of the quadratic function. $$f(x)=-3 x^{2}-18$$

Solve the quadratic equation by using the quadratic formula. Find only real solutions. $$-\frac{1}{3} x^{2}-3 x+9=0$$

Find the average rate of change of each ficnetion on the given interval. $$f(x)=2|x|+4 ; \text { interval: }[3,5]$$

Find the vertex and axis of symmetry of the associated parabola for each quadratic function. Sketch the parabola. Find the intervals on which the function is increasing and decreasing, and find the range. $$f(x)=2 x^{2}+4 x-3$$

In Exercises \(49-66,\) let \(f(x)=x^{2}+x, g(x)=\sqrt{x},\) and \(h(x)=-3 x\) Evaluate each of the following. $$(h \circ g)(4)$$

Solve the equation to find all real solutions. Check your solutions. $$3 x^{2 / 3}+2 x^{1 / 3}-1=0$$

Compute the zeros of the quadratic function. $$f(x)=-x^{2}-x-1$$

Solve the quadratic equation by using the quadratic formula. Find only real solutions. $$-0.75 x^{2}+2=2 x$$

Find the average rate of change of each ficnetion on the given interval. $$f(x)=|x|-5 ; \text { interval: }[-4,-2]$$

Find the vertex and axis of symmetry of the associated parabola for each quadratic function. Sketch the parabola. Find the intervals on which the function is increasing and decreasing, and find the range. $$g(x)=-4 x^{2}-8 x+5$$

In Exercises \(49-66,\) let \(f(x)=x^{2}+x, g(x)=\sqrt{x},\) and \(h(x)=-3 x\) Evaluate each of the following. $$(h \circ g)(0)$$

Solve the equation to find all real solutions. Check your solutions. $$2 x^{2 / 3}-5 x^{1 / 3}-3=0$$

Compute the zeros of the quadratic function. $$g(x)=x^{2}-x+1$$

Solve the quadratic equation by using the quadratic formula. Find only real solutions. $$0.25 x^{2}-0.5 x=1$$

Find the average rate of change of each ficnetion on the given interval. $$f(x)=\sqrt{-x} ; \text { interval: }[-4,-3]$$

Find the vertex and axis of symmetry of the associated parabola for each quadratic function. Sketch the parabola. Find the intervals on which the function is increasing and decreasing, and find the range. $$f(x)=-0.2 x^{2}+0.4 x-2.2$$

In Exercises \(49-66,\) let \(f(x)=x^{2}+x, g(x)=\sqrt{x},\) and \(h(x)=-3 x\) Evaluate each of the following. $$(g \circ h)(-3)$$

Use a graphing utility to find all real solutions. You may need to adjust the window size manually or use the ZOOMFIT feature to get a clear graph. $$\text { Solve } \sqrt{2.35-x}+1.8=2.75$$

Compute the zeros of the quadratic function. $$h(t)=3 t^{2}-2 t-9$$

Solve the quadratic equation using any method. Find only real solutions. $$x^{2}-4=0$$

Find the average rate of change of each ficnetion on the given interval. $$f(x)=\sqrt{x}+3 ; \text { interval: }[2,4]$$

Find the vertex and axis of symmetry of the associated parabola for each quadratic function. Sketch the parabola. Find the intervals on which the function is increasing and decreasing, and find the range. $$f(x)=0.3 x^{2}+0.6 x+1.3$$