Skip to main content
Ch. 3 - Polynomial and Rational Functions
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Lial 13th EditionCh. 3 - Polynomial and Rational Functions문제 17
4장, 문제 17

Match each function with its graph without actually entering it into a calculator. Then, after completing the exercises, check the answers with a calculator. Use the standard viewing window. ƒ(x) = (x + 4)2 - 3

검증된 단계별 안내
1
Identify the base function: recognize that the given function is a quadratic function in vertex form, which is \(f(x) = (x + 4)^2 - 3\). The base function is \(x^2\), a parabola opening upwards with vertex at the origin.
Determine the vertex of the parabola: since the function is in the form \(f(x) = (x - h)^2 + k\), the vertex is at \((-4, -3)\) because the expression inside the square is \((x + 4)\), which can be rewritten as \((x - (-4))\).
Analyze the transformations: the graph is shifted horizontally 4 units to the left (due to \(x + 4\)) and vertically 3 units down (due to \(-3\)). The parabola still opens upwards because the coefficient of the squared term is positive.
Sketch or visualize the graph based on these transformations: start with the basic parabola \(y = x^2\), move it left 4 units and down 3 units to place the vertex at \((-4, -3)\), and keep the shape the same (opening upwards).
Match the function to the graph that has a vertex at \((-4, -3)\) and opens upwards, without any stretching or reflecting, then verify your choice using a calculator with the standard viewing window.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
영상 길이:
3m
도움이 되었나요?

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Transformations of Quadratic Functions

Understanding how changes inside the function's formula affect its graph is essential. For f(x) = (x + 4)^2 - 3, the '+4' inside the parentheses shifts the graph horizontally left by 4 units, and the '-3' shifts it vertically down by 3 units. Recognizing these shifts helps match the function to its graph without graphing technology.
추천 영상:
4:22
Domain & Range of Transformed Functions

Standard Form and Vertex of a Parabola

A quadratic function in vertex form, f(x) = a(x - h)^2 + k, reveals the vertex directly as (h, k). Here, rewriting f(x) = (x + 4)^2 - 3 as (x - (-4))^2 - 3 shows the vertex at (-4, -3). Knowing the vertex location is key to identifying the parabola's position on the coordinate plane.
추천 영상:
04:34
Converting Standard Form to Vertex Form

Shape and Direction of Parabolas

The coefficient of the squared term determines the parabola's opening direction and width. Since the coefficient of (x + 4)^2 is positive 1, the parabola opens upward and has a standard width. This knowledge helps distinguish the graph from others that might open downward or be wider/narrower.
추천 영상:
5:28
Horizontal Parabolas
관련 실천
교과서 질문

Use synthetic division to perform each division. 13x3−29x2+227x−181x−13\(\frac{\frac{1}{3}\)x^3 - \(\frac{2}{9}\)x^2 + \(\frac{2}{27}\)x - \(\frac{1}{81}\)}{x - \(\frac{1}{3}\)}

532
views
교과서 질문

Solve each quadratic inequality. Give the solution set in interval notation. x2 + x - 30 ≤ 0

568
views
교과서 질문

Match each statement with its corresponding graph in choices A–D. In each case, k > 0. y varies directly as x. (y=kx)

695
views
교과서 질문

Use synthetic division to find ƒ(2). ƒ(x)=2x3-3x2+7x-12

472
views
교과서 질문

Use synthetic division to find ƒ(2). ƒ(x)=5x4-12x2+2x-8

474
views
교과서 질문

Use the factor theorem and synthetic division to determine whether the second polynomial is a factor of the first. x3+2x2+3; x-1

828
views