What is the vertex of the graph of g(x) = x^2 – 8x + 6?
The vertex of the graph of the quadratic function g(x) = x^2 – 8x + 6 can be found using the vertex formula or by completing the square. First, let’s identify the coefficients in the standard form of a quadratic function, which is g(x) = ax^2 + bx + c. Here, a = 1, b […]
Which statements are true about the graph of the function f(x) = x² – 8x – 5? Check all that apply.
To analyze the graph of the function f(x) = x² – 8x – 5, we can start by rewriting it in vertex form or by identifying key characteristics such as the vertex, axis of symmetry, and intercepts. 1. **Vertex**: The vertex of a quadratic function in standard form f(x) = ax² + bx + c […]
If a function is not continuous at a point, then it is not defined at that point?
This statement is not necessarily true. A function can be discontinuous at a point while still being defined at that point. Continuity at a point requires that three conditions be met: The function must be defined at that point. The limit of the function as it approaches that point must exist. The limit must equal […]
What is the inverse of the function f(x) = x^9 + 2?
To find the inverse of the function f(x) = x9 + 2, we first need to replace f(x) with y: y = x9 + 2 Next, we switch x and y, since the inverse function essentially swaps the roles of x and y: x = y9 + 2 Now, we solve for y. Start by […]
How to Find the Nth Term in a Sequence with No Constant Difference
Finding the nth term in a sequence without a constant difference can be a bit challenging, but it’s definitely manageable with the right approach. This generally involves recognizing the pattern or rule that governs the terms of the sequence. First, let’s understand what a sequence with no constant difference means. In simple terms, the difference […]
What is the probability that each hand has an ace when a deck of 52 cards is divided into 4 hands of 13 cards each?
To determine the probability that each of the 4 hands contains exactly one ace when dividing a standard deck of 52 cards into 4 hands of 13 cards each, let’s break down the problem. First, we note that there are a total of 4 aces in the deck, and we want to distribute these 4 […]
Find the next three terms in the sequence 3, 12, 21
To find the next three terms in the sequence, we first need to identify the pattern in the given numbers: 3, 12, 21. Let’s look at the differences between the consecutive terms: 12 – 3 = 9 21 – 12 = 9 We can see that the difference between the first and second term, and […]
How to Construct a Square with Sides of Length AB
To construct a square with sides of length AB, follow these steps: Draw Line Segment AB: Start by drawing a straight line segment that represents AB. Use a ruler for accuracy and label the endpoints as A and B. Construct Perpendicular Lines: At point A, use a compass and straightedge to construct a line that […]
How to Find the Arc Length with the Formula?
To find the arc length using the arc length formula, we first need to know the relationship between the angle, the radius, and the arc length. The formula for the arc length (s) is given by: s = r * θ Where: s is the arc length. r is the radius of the circle. θ […]
How to Solve the System of Equations: y = 2x^2 + 3 and y = 3x + 1?
To solve the system of equations given by y = 2×2 + 3 and y = 3x + 1, we will set the two equations equal to each other since they both equal y. Starting with the equations: y = 2×2 + 3 y = 3x + 1 Set them equal to each other: 2×2 […]