Which of the following functions best describes this graph?

For this case the function shown in the graph is:
[tex]y = (x-2) (x-2) [/tex]
To prove it, it is enough to check two solutions:

1) intersection with the y axis:
It happens when we evaluate the function for x = 0.
We have then:
[tex]y = (0-2) (0-2) y = (-2) (- 2) y = 4[/tex]
Therefore, the ordered pair intersection with the y-axis is:
[tex](x, y) = (0, 4) [/tex]
As you can see in the graph.

2) Cut point with the x axis:
It occurs when y = 0.
We have then:
[tex](x-2) (x-2) = 0 [/tex]
Thus,
[tex]x = 2[/tex] (With multiplicity 2)

Answer:
[tex]y = (x-2) (x-2) [/tex]
option A

johanrusli johanrusli · Answer 2 · 2019-07-21T14:17:32+02:00

The equation of the following graph is y = ( x - 2 ) ( x - 2 )

Further explanation

The quadratic function has the following general equation:

[tex]\large {\boxed {f(x) = ax^2 + bx + c} }[/tex]

If x₁ and x₂ are the roots of a function of a quadratic equation, then:

[tex]\large {\boxed {f(x) = a(x - x_1)(x - x_2) } }[/tex]

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 tackle the problem.

From the attached image, there are 2 points passed by the graph that are (0 , 4) and (2 , 0).

This graph only has one real root that is (2 , 0) → x₁ = x₂ = 2 .

We can find the function with the following formula:

[tex]y = a (x - x_1) (x - x_2)[/tex]

[tex]y = a (x - 2) (x - 2)[/tex]

The graph pass through ( 0 , 4 ) , then :

[tex]y = a (x - 2) (x - 2)[/tex]

[tex]4 = a (0 - 2) (0 - 2)[/tex]

[tex]4 = a (4)[/tex]

[tex]a = 4 \div 4 [/tex]

[tex]\boxed {a = 1}[/tex]

Conclusion:

[tex]y = 1 (x - 2) (x - 2)[/tex]

[tex]\large {\boxed {y = (x - 2) (x - 2)} }[/tex]

Learn more

The Discriminant for the Quadratic Equation : https://brainly.com/question/8196933
Quadratic Equations : https://brainly.com/question/10387593
Solving Quadratic Equations by Factoring : https://brainly.com/question/12182022

Answer details

Grade: College

Subject: Mathematics

Chapter: Quadratic Equations

Keywords: Equation , Line , Variable , Line , Gradient , Point , Quadratic , Intersection