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
2 answers:
The range of the function on the graph is:
all the real numbers greater than or equal to –3
<h3>Further explanation</h3>Discriminant of quadratic equation ( ax² + bx + c = 0 ) could be calculated by using :
<h2>D = b² - 4 a c</h2>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:
<h2>y = a ( x - h )² + k </h2><em>where : ( h, k ) → the turning point</em>
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 :
<h2>y = ( x - 2 )² - 3</h2>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 :
<h2>Range = { y | y ≥ -3 , y ∈ R }</h2>- Solving Quadratic Equations by Factoring : brainly.com/question/12182022
- Determine the Discriminant : brainly.com/question/4600943
- Formula of Quadratic Equations : brainly.com/question/3776858
Grade: High School
Subject: Mathematics
Chapter: Quadratic Equations
Keywords: Quadratic , Equation , Discriminant , Real , Number , Solution , Zero , Root
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