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