On a coordinate plane, a curved line crosses the y-axis at (0, 1), crosses the x-axis at (.25, 0), turns at point (2, negative 3), and crosses the x-axis (3.75, 0). What is the range of the function on the graph? all the real numbers all the real numbers greater than or equal to 0 all the real numbers greater than or equal to 2 all the real numbers greater than or equal to –3

Question

29-10-2019
Mathematics

contestada

On a coordinate plane, a curved line crosses the y-axis at (0, 1), crosses the x-axis at (.25, 0), turns at point (2, negative 3), and crosses the x-axis (3.75, 0). What is the range of the function on the graph? all the real numbers all the real numbers greater than or equal to 0 all the real numbers greater than or equal to 2 all the real numbers greater than or equal to –3

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calculista calculista · Answer 1 · 2019-11-12T10:38:47+01:00

calculista calculista

12-11-2019

Answer:

All real numbers greater than or equal to -3

Step-by-step explanation:

we know that

The curved line could be a vertical parabola opening upwards with vertex at (2,-3)

The vertex is a minimum

The y-intercept is the point (0,1)

The x-intercepts are the points (0.25,0) and (3.75,0)

so

The domain is the interval -----> (-∞,∞)

All real numbers

The range is the interval ----> [-3,∞)

All real numbers greater than or equal to -3

Answer Link

johanrusli johanrusli · Answer 2 · 2019-11-13T04:16:55+01:00

The range of the function on the graph is:

all the real numbers greater than or equal to –3

Further explanation

Discriminant of quadratic equation ( ax² + bx + c = 0 ) could be calculated by using :

D = b² - 4 a c

From the value of Discriminant , we know how many solutions the equation has by condition :

D < 0 → No Real Roots

D = 0 → One Real Root

D > 0 → Two Real Roots

Let us now tackle the problem!

Assume the curved line fits quadratic function with general equation:

y = a ( x - h )² + k

where : ( h, k ) → the turning point

[tex]\texttt{ }[/tex]

It is given that the turning point is ( 2 , - 3 ) , then:

y = a ( x - 2 )² - 3

The curved line crosses the y - axis at ( 0, 1 ) , then:

y = a ( x - 2 )² - 3

1 = a ( 0 - 2 )² - 3

1 + 3 = a ( -2 )²

4 = a ( 4 )

a = 4 ÷ 4

a = 1

The quadratic function could be approximated as :

y = ( x - 2 )² - 3

[tex]\texttt{ }[/tex]

From the attachment it could be concluded that the range of the function on the graph is :

All the real numbers greater than or equal to –3 , i. e :

Range = { y | y ≥ -3 , y ∈ R }

[tex]\texttt{ }[/tex]

Learn more

Solving Quadratic Equations by Factoring : https://brainly.com/question/12182022
Determine the Discriminant : https://brainly.com/question/4600943
Formula of Quadratic Equations : https://brainly.com/question/3776858

Answer details

Grade: High School

Subject: Mathematics

Chapter: Quadratic Equations

Keywords: Quadratic , Equation , Discriminant , Real , Number , Solution , Zero , Root