Math Problem Statement

First write the function in vertex form. Then find the function information below.

​(A) Intercepts

​(B) Vertex

​(C) Maximum or minimum

​(D) Range

​g(x)equals=0.35 x squared minus 0.7 x minus 90.35x2−0.7x−9

Question content area bottom

Part 1

Choose the correct vertex form below.

A.g left parenthesis x right parenthesis equals 0.35 left parenthesis x minus 1 right parenthesis squared minus 9

g left parenthesis x right parenthesis equals 0.35 left parenthesis x minus 1 right parenthesis squared minus 9g(x)=0.35(x−1)2−9

B.g left parenthesis x right parenthesis equals 0.35 left parenthesis x minus 0.35 right parenthesis squared minus 9.35

g left parenthesis x right parenthesis equals 0.35 left parenthesis x minus 0.35 right parenthesis squared minus 9.35g(x)=0.35(x−0.35)2−9.35

C.g left parenthesis x right parenthesis equals 0.35 left parenthesis x minus 1 right parenthesis squared minus 9.35

g left parenthesis x right parenthesis equals 0.35 left parenthesis x minus 1 right parenthesis squared minus 9.35g(x)=0.35(x−1)2−9.35

D.g left parenthesis x right parenthesis equals 0.35 left parenthesis x minus 0.35 right parenthesis squared minus 9

g left parenthesis x right parenthesis equals 0.35 left parenthesis x minus 0.35 right parenthesis squared minus 9g(x)=0.35(x−0.35)2−9

Part 2

​(A) What​ is/are the​ x-intercept(s) of the function​ g(x)? Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

A.

The function​ g(x) has no​ x-intercepts.

B.

The function​ g(x) has​ x-intercept(s)

enter your response here.

​(Type an integer or decimal rounded to two decimal places as needed. Use a comma to separate answers as​ needed.)

Part 3

What​ is/are the​ y-intercept(s) of the function​ g(x)? Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

A.

The function​ g(x) has​ y-intercept(s)

enter your response here.

​(Type an integer or decimal rounded to two decimal places as needed. Use a comma to separate answers as​ needed.)

B.

The function​ g(x) has no​ y-intercepts.

Part 4

​(B) What is the vertex of the graph of​ g(x)?

enter your response here

​(Type an ordered​ pair.)

Part 5

​(C) The function​ g(x) has a

▼   maximum

minimum

value of

enter your response here.

Part 6

​(D) What is the range of​ g(x)?

enter your response here

​(Type your answer in interval​ notation.)

Choose the correct vertex form below.input field 1Select the correct choice below and, if necessary, fill in the answer box to complete your choice.input field 2Select the correct choice below and, if necessary, fill in the answer box to complete your choice.(B) What is the vertex of the graph of g(x)?(Type an ordered pair.)(C) The function g(x) has avalue ofvalue of.(D) What is the range of g(x)?(Type your answer in interval notation.)

Solution

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Math Problem Analysis

Mathematical Concepts

Algebra
Quadratic Functions
Vertex Form
Intercepts
Parabolas

Formulas

Vertex form of a quadratic function: g(x) = a(x - h)^2 + k
Quadratic equation formula for finding x-intercepts: ax^2 + bx + c = 0

Theorems

Vertex Theorem for Quadratic Functions

Suitable Grade Level

Grades 9-12