Skip to main content
Ch. 3 - Polynomial and Rational Functions
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoBlitzer 8th EditionCh. 3 - Polynomial and Rational FunctionsProblema 15
Capitolo 4, Problema 15

Find the coordinates of the vertex for the parabola defined by the given quadratic function. f(x)=−x2−2x+8

Guida verificata passo dopo passo
1
Identify the quadratic function given: \(f(x) = -x^2 - 2x + 8\). This is in the standard form $f(x) = ax^2 + bx + c$ where \(a = -1\), \(b = -2\), and \(c = 8\).
Recall that the vertex of a parabola defined by $f(x) = ax^2 + bx + c$ has an \(x\)-coordinate given by the formula \(x = -\frac{b}{2a}\).
Substitute the values of \(a\) and \(b\) into the vertex formula: \(x = -\frac{-2}{2 \times -1}\).
Simplify the expression to find the \(x\)-coordinate of the vertex.
To find the \(y\)-coordinate of the vertex, substitute the \(x\)-value back into the original function: \(f(x) = -x^2 - 2x + 8\). Calculate \(f(\text{x-coordinate})\) to get the \(y\)-coordinate.

Risposta video verificata per un problema simile:

Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.
Durata del video:
3m

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

Quadratic Functions

A quadratic function is a polynomial of degree two, generally written as f(x) = ax^2 + bx + c. Its graph is a parabola, which can open upwards or downwards depending on the sign of the coefficient a.
Video consigliato:
06:36
Solving Quadratic Equations Using The Quadratic Formula

Vertex of a Parabola

The vertex is the highest or lowest point on the parabola, representing its maximum or minimum value. For f(x) = ax^2 + bx + c, the vertex's x-coordinate is found using -b/(2a), and the y-coordinate is f(-b/(2a)).
Video consigliato:
5:28
Horizontal Parabolas

Evaluating Functions

Evaluating a function means substituting a specific value for the variable and calculating the result. To find the vertex's y-coordinate, substitute the x-value of the vertex into the original quadratic function.
Video consigliato:
4:26
Evaluating Composed Functions
Pratica correlata
Domanda del libro di testo

Solve each polynomial inequality in Exercises 1–42 and graph the solution set on a real number line. Express each solution set in interval notation. 3x2+16x<−53x^2+16x<−5

526
views
Domanda del libro di testo

In Exercises 15–18, use the Leading Coefficient Test to determine the end behavior of the graph of the given polynomial function. Then use this end behavior to match the polynomial function with its graph. [The graphs are labeled (a) through (d).] <IMAGE>

f(x)=−x4+x2f(x)=−x^4+x^2

726
views
Domanda del libro di testo

Use the graph of the rational function in the figure shown to complete each statement in Exercises 15–20.

As x→1+, f(x)→x\(\to\)1^{+},\(\text{ }\)f(x)\(\to\) __

1054
views
Domanda del libro di testo

Divide using long division. State the quotient, and the remainder, r(x). (x4+2x3−4x2−5x−6)/(x2+x−2)

604
views
Domanda del libro di testo

Divide using long division. State the quotient, and the remainder, r(x).2x5−8x4+2x3+x22x3+1\(\frac{2x^5 - 8x^4 + 2x^3 + x^2}{2x^3 + 1}\)

530
views
Domanda del libro di testo

Write an equation that expresses each relationship. Then solve the equation for y. x varies jointly as y and z and inversely as the square root of w.

594
views