Question

Which of the following functions best describes this graph?

Answer 1

For this case the function shown in the graph is:
 $y = (x-2) (x-2)$
 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:
 $y = (0-2) (0-2) y = (-2) (- 2) y = 4$
 Therefore, the ordered pair intersection with the y-axis is:
 $(x, y) = (0, 4)$
 As you can see in the graph.

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

 Answer:
 $y = (x-2) (x-2)$
 option A

Answer 2

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

Further explanation

The quadratic function has the following general equation:

$\large {\boxed {f(x) = ax^2 + bx + c} }$

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

$\large {\boxed {f(x) = a(x - x_1)(x - x_2) } }$

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:

$y = a (x - x_1) (x - x_2)$

$y = a (x - 2) (x - 2)$

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

$y = a (x - 2) (x - 2)$

$4 = a (0 - 2) (0 - 2)$

$4 = a (4)$

$a = 4 \div 4$

$\boxed {a = 1}$

Conclusion:

$y = 1 (x - 2) (x - 2)$

$\large {\boxed {y = (x - 2) (x - 2)} }$

Learn more

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

Answer details

Grade: College

Subject: Mathematics

Chapter: Quadratic Equations

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