Chapter 10

For the following problems, solve the equations. $$ (x-2)(x-5)=0 $$

Specify the values of \(a, b,\) and \(c\). $$ 2 y^{2}-3 y+10=0 $$

Use the idea suggested in Sample Set A to sketch (quickly and perhaps not perfectly accurately) the graphs of $$ y=x^{2}+1 \quad \text { and } \quad y=x^{2}-3 $$

Determine the values of \(a, b,\) and \(c\) in the following quadratic equations. $$ 4 x^{2}-3 x+5=0 $$

Solve each of the following quadratic equations using the method of extraction of roots. $$ x^{2}-144=0 $$

Solve the following equations, if possible. $$ (x-7)(x+4)=0 $$

Which of the following equations are quadratic equations? Answer "yes" or "no" to each equation. $$ 6 x^{2}-4 x+9=0 $$

For the following problems, solve the equations. $$ (b+1)(b-6)=0 $$

It is estimated that \(t\) years from now the population of a particular city will be \(P=t^{2}-24 t+96,000\) How many years from now will the population be \(95,865 ?\)

Use the idea suggested in Sample Set \(\mathrm{B}\) to sketch the graphs of $$ y=(x-3)^{2} \quad \text { and } \quad y=(x+1)^{2} $$

Determine the values of \(a, b,\) and \(c\) in the following quadratic equations. $$ 3 y^{2}-2 y+9=0 $$

Solve each of the following quadratic equations using the method of extraction of roots. $$ 9 y^{2}-121=0 $$

Solve the following equations, if possible. $$ (2 x+5)(5 x-7)=0 $$

For the following problems, solve the equations. $$ (a+10)(a-5)=0 $$

The length of a rectangle is 3 feet more than twice its width. The area is 14 square feet. Find the dimensions.

Graph \(y=(x-2)^{2}+1\).

Use the zero-factor property to solve each quadratic equation. $$ (3 x+5)(x-1)=0 $$

Determine the values of \(a, b,\) and \(c\) in the following quadratic equations. $$ x^{2}-5 x-1=0 $$

Solve each of the following quadratic equations using the method of extraction of roots. $$ 6 a^{2}=108 $$

Solve the following equations, if possible. $$ x^{2}+2 x-24=0 $$

For the following problems, solve the equations. $$ (y-3)(y-4)=0 $$

The area of a triangle is 24 square meters. The base is 2 meters longer than the height. Find the base and height. The formula for the area of a triangle is \(A=\frac{1}{2} b \cdot h\)

For the following problems, graph the quadratic equations. $$ y=x^{2} $$

Use the zero-factor property to solve each quadratic equation. $$ 3 b(2 b-1)=0 $$

Determine the values of \(a, b,\) and \(c\) in the following quadratic equations. $$ z^{2}-4=0 $$

Solve each of the following quadratic equations using the method of completing the square. $$ 5 y^{2}-2 y-4=0 $$

Which of the following equations are quadratic equations? Answer "yes" or "no" to each equation. $$ 4 x^{2}-2 x+4=1 $$

Solve the following equations, if possible. $$ 6 x^{2}+13 x-5=0 $$

The product of two consecutive integers is 210 . Find them.

For the following problems, graph the quadratic equations. $$ y=-x^{2} $$

Use the zero-factor property to solve each quadratic equation. $$ (a-8)^{2}=0 $$

Determine the values of \(a, b,\) and \(c\) in the following quadratic equations. $$ x^{2}-2 x=0 $$

Solve \(5 p^{2} q^{2}=45 p^{2}\) for \(q\).

Which of the following equations are quadratic equations? Answer "yes" or "no" to each equation. $$ \frac{2}{x}-5 x^{2}=6 x+4 $$

Solve the following equations, if possible. $$ 5 y^{2}+2 y=3 $$

For the following problems, solve the equations. $$ (m-8)(m+1)=0 $$

For the following problems, solve the equations. $$ (4 y+1)(2 y+3)=0 $$

Four is added to an integer and that sum is tripled. When this result is multiplied by the original integer, the product is -12 . Find the integer.

Solve each quadratic equation by factoring. $$ 4 x^{2}-16=0 $$

For the following problems, graph the quadratic equations. $$ y=(x-1)^{2} $$

For the following problems, solve the equations by completing the square. $$ x^{2}+2 x-8=0 $$

Solve \(16 m^{2}-2206=0 .\) Round to the nearest hundredth.

Which of the following equations are quadratic equations? Answer "yes" or "no" to each equation. $$ 9 x^{2}-2 x+6=4 x^{2}+8 $$

Solve the following equations, if possible. $$ m(2 m-11)=0 $$

For the following problems, solve the equations. $$ (x+2)(3 x-1)=0 $$

Solve each quadratic equation by factoring. $$ y^{2}-12 y+32=0 $$

For the following problems, graph the quadratic equations. $$ y=(x-2)^{2} $$

Determine the values of \(a, b,\) and \(c\) in the following quadratic equations. $$ 2 x^{2}-4 x=-1 $$

For the following problems, solve the equations by completing the square. $$ y^{2}-5 y-6=0 $$

Use the zero-factor property to solve each equation. $$ 6(a-4)=0 $$