🧮 algebra

1. The problem is to understand the vertex form of a quadratic function, which is given by the formula: $$y = a(x - h)^2 + k$$

1. The problem is to factor each polynomial expression by finding the greatest common factor (GCF) and simplifying. 2. The formula for factoring by GCF is: $$a \cdot b + a \cdot c

1. The problem is to simplify the polynomial expression by distributing the factor outside the parentheses to each term inside the parentheses. 2. The general formula for distribut

1. The problem asks which set of ordered pairs $(x, y)$ could represent a linear function. 2. A linear function has a constant slope between any two points. The slope formula betwe

1. **State the problem:** We need to find the area $A$ of a square with side length $s = 4m^2n^4$. 2. **Formula:** The area of a square is given by the formula:

1. **State the problem:** Simplify the expression $$(x^3 y^{-3}) (2 x^5 y^4)^3$$. 2. **Recall the rules:**

1. **State the problem:** Simplify the expression $$\left(\frac{x^3 y^2}{z^4}\right)^2$$. 2. **Recall the power of a quotient rule:** When raising a fraction to a power, raise both

1. **State the problem:** Simplify the expression $$6 \left( \frac{x^3 y^{12}}{z^4} \right)^2 \cdot \frac{x^5}{1}$$. 2. **Recall the exponent rules:**

1. **State the problem:** Multiply the expressions $(-2x)$ and $(3x^4)$. 2. **Write the multiplication:** $$(-2x)(3x^4)$$

1. **State the problem:** Simplify the expression $$(2a^2bc^3)^4$$. 2. **Recall the power of a product rule:** When raising a product to a power, raise each factor to that power:

1. **State the problem:** Simplify the expression $ (2a^2bc^3)^4 $. 2. **Recall the power of a product rule:** When raising a product to a power, raise each factor to that power: $

1. **State the problem:** Translate the sentence "The sum of 3 and y is less than or equal to -20" into an inequality. 2. **Identify the sum:** The sum of 3 and y is written as $3

1. **State the problem:** Translate the sentence "Two more than the product of a number and 6 is equal to 7" into an equation using the variable $b$ for the unknown number. 2. **Id

1. **State the problem:** We are given the midpoint M(65.5, 58.5) of segment ST and one endpoint S(66, 19). We need to find the coordinates of the other endpoint T(x, y). 2. **Form

1. **State the problem:** We are given the midpoint $M$ of segment $CD$ with coordinates $(1.5, -12.5)$ and one endpoint $C$ with coordinates $(5, -18)$. We need to find the coordi

1. **State the problem:** We are given the midpoint $M(11.5, 4)$ of segment $VW$ and one endpoint $V(9, 3)$. We need to find the coordinates of the other endpoint $W$. 2. **Formula

1. **State the problem:** We are given the zeros, axis of symmetry, max or min value, and vertex of a quadratic function. We need to verify these characteristics for the first quad

1. **State the problem:** Simplify the expression $$\frac{p}{2} - (q + p - (2 + q))$$ and then substitute $p=2$ and $q=10$. 2. **Write the expression:**

1. The problem is to match parabolas of the form $y = ax^2 + bx + c$ with their $a$-values based on the shape and direction of their graphs. 2. Recall that the coefficient $a$ dete

1. The problem is to match parabolas with their corresponding $a$-values in the quadratic function $y = ax^2 + bx + c$. 2. The value of $a$ determines the direction and steepness o

1. **Problem Statement:** Graph and compare the functions $y = x^2 + 3$, $y = (x + 3)^2$, and $y = x^2$. Identify similarities and differences.