🧮 algebra

1. **State the problem:** Expand the function $y=2(x-3)^2+6$ to general form and find its range. 2. **Recall the formula:** The general form of a quadratic function is $y=ax^2+bx+c

1. **State the problem:** Write a quadratic function in factored form with x-intercepts $\left(-\frac{1}{4}, 0\right)$ and $(8, 0)$ that passes through the point $(0, 2)$. 2. **Rec

1. **State the problem:** A sea otter's position changes by $-73.5$ feet in 3 minutes. We need to find the average change in position per minute. 2. **Formula:** Average change per

1. The problem is to determine whether a given solution is extraneous or not. 2. An extraneous solution is a solution that emerges from the process of solving the equation but does

1. **State the problem:** Solve the equation $$\frac{4}{x} + 1 = \frac{5}{3}$$ for $x$. 2. **Isolate the fraction:** Subtract 1 from both sides:

1. **State the problem:** Vincent, Nari, and Lizbeth play a carnival game. Vincent's score is $-35$ points. Nari's score is $\frac{3}{7}$ of Vincent's score.

1. **State the problem:** Vincent, Nari, and Lizbeth play a carnival game. Vincent's score is $-35$ points. Nari's score is $\frac{3}{7}$ of Vincent's score. Lizbeth scores $\frac{

1. **State the problem:** We are given the number of crimes committed in 2011 and the percentage increase from 2011 to 2012 for three places. We need to find the number of crimes c

1. **State the problem:** A video has $4 \times 10^8$ views in total, and 3% of these views are from Italy. We need to find how many views come from Italy and express the answer in

1. Il problema chiede di risolvere l'espressione $$\left[\left(\frac{3}{4} - \frac{1}{2}\right)^2 \left(\frac{1}{2} - \frac{1}{4}\right)(-3)^2 - 1\right] + (-3)2 - 1$$. 2. Calcolia

1. **State the problem:** Calculate the value of $$4^2 - \left(\frac{2}{3}\right)^2 + \left(-\frac{3}{2}\right)^2 \times \frac{1}{3}$$. 2. **Recall the rules:**

1. **State the problem:** Simplify the expression $x[x^2 + 3]$. 2. **Recall the distributive property:** For any numbers $a$, $b$, and $c$, $a(b + c) = ab + ac$.

1. The problem asks us to analyze the graph of Jason's height above the ground during a Ferris wheel ride over time and determine which statements about the function are correct. 2

1. **State the problem:** Factorise fully the quadratic expression $$6y^2 - 5y - 4$$. 2. **Recall the factoring formula:** For a quadratic $$ay^2 + by + c$$, we look for two number

1. **State the problem:** We are given a piecewise linear function with two segments intersecting at $x=0$. The left segment goes from $(-2,3)$ to $(0,-4)$ and the right segment go

1. **State the problem:** We need to find the equation that represents the water level $w$ after $d$ days based on the given data points: $(3, 96)$, $(6, 90)$, $(9, 84)$, $(12, 78)

1. The problem states that the curve $y=f(x)$ has a minimum point at $(5,-4)$. 2. We need to find the coordinates of the minimum point on the curve $y=f(x+7)$.

1. **State the problem:** Simplify the expression $\frac{4}{5} + \frac{2}{3} \times 4$. 2. **Recall the order of operations:** Multiplication must be done before addition.

1. **Problem statement:** We need to find a linear function that converts the highest mark 285 to 200 and the lowest mark 75 to 60. 2. **Formula and explanation:** A linear functio

1. The problem asks to calculate the value of the expression $x - 3$ for two values of $x$: a) $x=2$ and b) $x=7$. 2. The formula used is simply substitution: replace $x$ with the

1. **Problem statement:** Find a formula for the sum $$\sum_{i=1}^x i$$ assuming $x$ is even. 2. **Recall the problem:** We want to find a closed-form expression for the sum of the