1.
Is the given point on the graph of \(y^2 = x^3 - 10 x + 3\text{?}\) How can you be sure?
- \(\displaystyle (3,0)\)
- \(\displaystyle (0,3)\)
- \(\displaystyle (0,\sqrt{3})\)
- \(\displaystyle (\sqrt{3},0)\)
- \(\displaystyle (1,2)\)
Exercises 5.8 Exercises
2.
Find an equation for the circle having the points \((-2,4)\) and \((7,9)\) as endpoints of a diameter.
Linear Equations.
3.
Sketch a graph of each equation.
- \(\displaystyle x=-4\)
- \(\displaystyle y=3\)
- \(\displaystyle 2y=-1\)
4.
What is an equation for the \(x\)-axis? What is an equation for the \(y\)-axis?
5.
Find the intercepts of \(4x-7y = 2\) and sketch its graph.
6.
Sketch a graph of \(y - 7 = -2 (x+1)\)
7.
Find a linear equation for the line passing through the points \((5,4)\) and \((-2,3)\text{.}\)
8. Linear Models.
Let \(C\) denote the annual cost in millions of dollars to maintain a computer network \(t\) years since the year 2000 (so that \(t = 0\) corresponds to the year 2000). In 2005, it cost 2 million dollars and, in 2010 it cost 17 million dollars.
- At what rate is the cost increasing per year, assuming the rate of increase remains constant?
- Find a linear model for the cost \(C\text{.}\)
- Use your model to predict the cost to maintain the network in 2020.
9. A Parabola.
Find an equation for the parabola with focus at \(F(0,-1)\) and directrix \(y = 2\text{.}\)
