🧮 algebra

1. The problem asks to translate the graph of $y = x^2$ to get the graph of $y = x^2 - 2$. 2. The formula for vertical translation of a function $f(x)$ is $f(x) + k$, where $k$ is

1. **State the problem:** We are given the quadratic function $f(x) = -x^2 + 8x - 1$ and need to find the intercepts, vertex, and axis of symmetry.

1. **State the problem:** We are given the linear equation $$-2x + 5y = 20$$ and want to understand its graph and intercepts. 2. **Rewrite the equation to slope-intercept form:** S

1. The problem is to graph the line given by the equation $$y = \frac{1}{3}x + 7$$ on a Cartesian coordinate grid. 2. The equation is in slope-intercept form $$y = mx + b$$ where $

1. The problem is to graph the line given by the equation $y = -2x + 1$. 2. This is a linear equation in slope-intercept form $y = mx + b$, where $m$ is the slope and $b$ is the y-

1. **State the problem:** We need to graph the line given by the equation $$y = \frac{1}{5}x - 5$$ on a Cartesian coordinate system. 2. **Recall the slope-intercept form:** The equ

1. Stating the problem: Simplify the expression $$-\frac{2}{9} + \left(-\frac{1}{3}\right)$$. 2. Formula and rules: To add or subtract fractions, they must have a common denominato

1. **State the problem:** Find an equivalent expression for $g^2 (7 + h)$ using the Distributive Property. 2. **Recall the Distributive Property:** For any numbers or variables $a$

1. The problem is to graph the line given by the equation $$y = -\frac{1}{2}x + 7$$ on a coordinate plane. 2. The equation is in slope-intercept form $$y = mx + b$$ where $$m$$ is

1. **State the problem:** We need to find the quotient when dividing the polynomial $6x^3 - 43x^2 - 34x + 4$ by $6x + 5$. 2. **Recall the division formula:** Polynomial division is

1. **State the problem:** Simplify the ratio $$\sqrt{12} : \sqrt{300} : \sqrt{48}$$ to its simplest form. 2. **Recall the rule:** The ratio of square roots can be simplified by exp

1. The problem is to simplify the ratio $$\sqrt{12} : \sqrt{300} : \sqrt{48}$$. 2. Recall that the square root of a product can be written as the product of square roots: $$\sqrt{a

1. **Problem:** Factor the trinomial $$45x^2 - 255xy + 350y^2$$ completely. 2. **Step 1: Identify the coefficients.**

1. **State the problem:** Find the vertical asymptotes (VA) of the function $$f(x)=\frac{x^2+2x-3}{x^2-1}$$. 2. **Recall the rule for vertical asymptotes:** Vertical asymptotes occ

1. **State the problem:** We need to find the rate of change of Tristan's earnings, which is the slope of the line passing through the points $(10, 248)$ and $(20, 496)$. 2. **Form

1. **State the problem:** We are given a table showing miles traveled ($x$) and total cost ($y$). We want to find the rate of change, which is the slope of the linear relationship

1. The problem asks to find an expression equivalent to $$\frac{2^{-1}}{2^4}$$. 2. Recall the rule for dividing powers with the same base: $$\frac{a^m}{a^n} = a^{m-n}$$.

1. The problem asks to find an expression equivalent to $$\frac{3^4}{3^8}$$. 2. Recall the rule for dividing powers with the same base: $$\frac{a^m}{a^n} = a^{m-n}$$.

1. **State the problem:** Simplify the expression $$(3f - 7)(5)$$. 2. **Use the distributive property:** Multiply each term inside the parentheses by 5.

1. **State the problem:** We need to find the domain and range of the given function, determine if it is invertible, justify the invertibility, and if invertible, find the domain a

1. **State the problem:** We need to evaluate the expression where the first two rational numbers are added instead of multiplied. Suppose the original expression was $\frac{a}{b}