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# Problems in Algebra - Quadratics and Graphing

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Practice problems in Algebra, including mostly quadratics and graphing. See the attached questions file.

1). Rationalize the denominator and simplify

2). Solve for , where t is a real number. If there is more than one solution, separate them with commas.

3). Solve for where x is a real number. If there is more than one solution, separate them with commas.

4) What is the value of ?
5). Write expression in simplified radical form
6).Find the roots of the quadratic equation. If there is more than one root, separate them with commas.

7). Solve the equation for If there is more than one solution, separate them with commas.

8). Solve where is a real number. Simplify as much as possible. If there is more than one solution, separate them with commas.
9). Solve for by using quadratic formula. If there is more than one solution, separate them with commas.

10). Graph the parabola. .
11). Graph the parabola.
12). Graph the parabola.
13) Find the intercept(s) and the coordinates of the vertex for the parabola If there is more than one intercept, separate them with commas.
14). Solve: If there is more than one solution, separate them with commas.
15). Solve the equation for If there is more than one solution, separate them with commas.

16) Compute the value of the discriminant and give the number of real solutions to the quadratic equation.

17). Solve for where is a real number. If there is more than one solution, separate them with commas.
A).
B).
18) Solve for where is a real number. If there is more than one solution, separate them with commas.

19. Factor completely:
A).
B).

20) Order the expressions by choosing .
A)
B)

21). Simplify. Write answer without using negative exponents.

22) Write in scientific notation
)

#### Solution Preview

The solution file is attached.

1). Rationalize the denominator and simplify

Ö(15/55) = Ö(3/11) = Ö3 /Ö11 = [Ö3 * Ö11]/(11) = Ö33 /11

2). Solve for , where t is a real number. If there is more than one solution, separate them with commas.

Ö(t - 22) = 5  t - 22 = 5^2 = 25  t = 25 + 22 = 47

3). Solve for where x is a real number. If there is more than one solution, separate them with commas.

Squaring on both sides, we get 6x + 7 = 9x - 10
3x = 17  x = 17/3

4) What is the value of ?
Given expression = 125^(1/3) = (5^3)^(1/3) = 5

5). Write expression in simplified radical form
3Ö54 = 3Ö(27 * 2) = 3Ö27 * 3Ö2 = 33Ö2

6).Find the roots of the quadratic equation. If there is more than one root, separate them with commas.

y^2 - 6y + y - 6 = 0
y(y - 6) + 1(y - 6) = 0
(y + 1)(y - 6) = 0
y = {-1, 6}

7). Solve the equation for If there is more than one solution, separate them ...

#### Solution Summary

Each problem has been worked out showing all working steps.

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