Master Algebra 1 Word Problems with our Comprehensive Practice

${\displaystyle y={(x+4)}^2-7}$
a) Determine the x-intercepts of the quadratic equation in both approximate and exact form
b) Determine the vertex point.
c) Determine the y-intercept.
d) Graph the parabola.

To solve:
${\displaystyle x^2+11x+24=0}$

How do you simplify 1 over square root 2?

To determine:
${\displaystyle 13x-15x+8=4x+2-24}$

To solve: ${\displaystyle \frac{4t^2}{5}=\frac{t}{5}+\frac{3}{10}}$

To solve: ${\displaystyle 4x^2=\frac{15}{2}x+1}$

To solve: ${\displaystyle \frac{n+1}{8}-\frac{2-n}{3}=\frac{5}{6}}$

Factor each of the algebraic expressions completely. ${\displaystyle 12x^3-52x^2-40x}$

Write the equation of the line with an undefined slope and goes through point ${\displaystyle (2,4)}$

How do you find the roots of ${\displaystyle x^3-12x+16=0}$ ?

How do you find the inverse of ${\displaystyle y=(-\frac{1}{2})x+7}$?

Andreas buys a new sailboat for $15,540. He estimates that the boat will depreciate by 5% each year. Which exponential function models this situation?
F. ${\displaystyle y=15,540{\left(1.05\right)}^x}$
G. ${\displaystyle y=15,540{\left(0.95\right)}^x}$
H. ${\displaystyle y=-15,540{\left(0.95\right)}^x}$
J. ${\displaystyle y=-15,540{\left(1.05\right)}^x}$

Write an algebraic expression to represent each verbal expression. Five more than the quotient of a number and 4

Does an algebraic expression have a single value? Explain?

It takes a person 50 minutes to get to campus. He spends t minutes walking to the bus stop and the rest of the time riding the bus. His walking rate is 0.06 miles per minute and the bus travels at a rate of 0.5 miles per minute. The total distance walking and traveling by bus is given by the algebraic expression ${\displaystyle 0.06t+0.5(50-1)}$.
(a) Simplify the algebraic expression (b) Use each form of the algebraic expression to determine the total distance that the person travels if the person spends 20 minutes walking to the bus stop.
(a) The simplified expression is. (Do not factor.) (b) Using the given expression, it is found that the total distance that the person travels is miles if he spends 20 minutes walking to the bus stop. Using the simplified expression, it is found that the total distance that the person travels is miles if the person spends 20 minutes walking to the bus stop.

Show that no finite field is algebraically closed

The sum of the first n odd natural numbers is equal to ${\displaystyle n^2}$

Otto's rectangular garden measures 12 feet by 20 feet. He decides to add a uniform width walkway around it. If the walkway and the garden together cover an area of 660 square feet, what is the width of the walkway? (Use algebra)

The length of a rectangle is 4 less than twice the width. The area of the rectangle is 70 square feet. Find the width, w, of the rectangle algebraically. Explain why one of the solutions for w is not viable.

Solve ${\displaystyle x^6-7x^3-8=0}$ algebraically. Find real solutions only, if they exist.