10.7 Graphing quadratic solutions

Use the idea suggested in Sample Set A to sketch (quickly and perhaps not perfectly accurately) the graphs of

$$\begin{array}{lllll}y=x^2+1\hfill & \hfill & \text{and}\hfill & \hfill & y=x^2-3\hfill \end{array}$$

  

Use the idea suggested in Sample Set B to sketch the graphs of

$$\begin{array}{lllll}y={\left(x-3\right)}^2\hfill & \hfill & \text{and}\hfill & \hfill & y={\left(x+1\right)}^2\hfill \end{array}$$

Graph $y={\left(x-2\right)}^2+1$

$y=x^2$

$y=-x^2$

$y={\left(x-1\right)}^2$

$y={\left(x-2\right)}^2$

$y={\left(x+3\right)}^2$

$y={\left(x+1\right)}^2$

$y=x^2-3$

$y=x^2-1$

$y=x^2+2$

$y=x^2+\frac{1}{2}$

$y=x^2-\frac{1}{2}$

$y=-x^2+1$ (Compare with problem 2.)

$y=-x^2-1$ (Compare with problem 1.)

$y={\left(x-1\right)}^2-1$

$y={\left(x+3\right)}^2+2$

$y=-{\left(x+1\right)}^2$

$y=-{\left(x+3\right)}^2$

$y=2x^2$

$y=3x^2$

$y=\frac{1}{2}{x}^2$

$y=\frac{1}{3}{x}^2$

( [link] ) Simplify and write ${\left(x^{-4}{y}^5\right)}^{-3}{\left(x^{-6}{y}^4\right)}^2$ so that only positive exponents appear.

( [link] ) Factor $y^2-y-42.$

( [link] ) Find the sum: $\frac{2}{a-3}+\frac{3}{a+3}+\frac{18}{a^2-9}.$

( [link] ) Simplify $\frac{2}{4+\sqrt{5}}.$

( [link] ) Four is added to an integer and that sum is doubled. When this result is multiplied by the original integer, the product is $-6.$ Find the integer.