🧮 algebra

1. The problem is to find the axis of symmetry for the quadratic function $-2x^2 + 6x - 3$. 2. The axis of symmetry for a quadratic function in the form $ax^2 + bx + c$ is given by

1. **State the problem:** Find the maximum point of the quadratic function $f(x) = -2x^2 + 6x - 3$. 2. **Formula and rules:** For a quadratic function $ax^2 + bx + c$, the vertex (

1. **State the problem:** Find the maximum and minimum points of the quadratic function $f(x) = -2x^2 + 6x - 3$. 2. **Formula and rules:** For a quadratic function $f(x) = ax^2 + b

1. **State the problem:** Find the maximum and minimum points of the function $y = -4x + 6$. 2. **Formula and rules:** This is a linear function of the form $y = mx + b$, where $m

1. **State the problem:** We know that $y$ varies inversely as $x$, which means $y = \frac{k}{x}$ for some constant $k$. Given $y=8$ when $x=3$, find the constant $k$. Then find $x

1. **State the problem:** Explain how we got the term $9n$ in the equation. 2. **Recall the step before:** We had the equation $n - \frac{1}{n} = 9$.

1. **State the problem:** Solve the equation $$\frac{n \times n \times n - n}{n^2} = 9$$ for $n$. 2. **Rewrite the expression:** The numerator is $n \times n \times n - n = n^3 - n

1. Let's start by understanding what "Checkpoint math stage 9" typically covers. It usually includes topics like algebra, geometry, number operations, and basic problem-solving ski

1. The problem is to understand why $x^3$ is not the leading term in the polynomial $x^5 + x^3 - x + 5$. 2. The leading term of a polynomial is the term with the highest exponent o

1. **State the problem:** We need to graph and find the feasibility region for the system of inequalities: 1) $5 + 3x \leq 2 + 4x$

1. The problem is to find the size or leading term of the polynomial function $$x^5 + x^3 - x + 5$$. 2. The leading term of a polynomial is the term with the highest power of $x$.

1. **Problem Statement:** Given that $y$ varies inversely as $x$, and $y=8$ when $x=3$, find the constant of variation $k$, and the value of $x$ when $y=12$. Also, find the variati

1. **State the problem:** We are given the function $f(x) = 2x^2 - 5x + 1$ and need to evaluate the difference quotient $$\frac{f(a+h) - f(a)}{h}$$ where $h \neq 0$. 2. **Recall th

1. The problem asks what happens if $i = 1$. 2. Normally, $i$ is defined as the imaginary unit where $i = \sqrt{-1}$ and $i^2 = -1$.

1. The problem asks what happens if $i = 1$. 2. Here, $i$ is often used to represent the imaginary unit, which is defined as $i = \sqrt{-1}$.

1. **State the problem:** Jacques has a weekly budget of 24 to spend on candy bars and eggs. Candy bars cost 2 per pack, eggs cost 6 per dozen. We want to find how many packs of ca

1. The problem is to understand what factorials are and how to calculate them. 2. The factorial of a non-negative integer $n$, denoted by $n!$, is the product of all positive integ

1. **Problem statement:** You asked if the operation involves multiplying a number by $n - 1$.

1. The problem is to understand how factorial works and see an example. 2. The factorial of a non-negative integer $n$, denoted by $n!$, is the product of all positive integers les

1. **Problem statement:** We want to express the total liters of oil produced in 2023, approximately $1.0435 \times 10^{11}$ liters, in words.

1. **Problem Statement:** We want to find the domain of the function $f(x) = \frac{x^2}{x^2 + 4}$. The domain is the set of all $x$ values for which the function is defined. 2. **K