Question

Which of the following functions best describes this graph?O A. y=x2- 8x+15O B. y=x+8x+15O c. y = x + x - 12O D. y=x2-5x+6

Answer 1

We will investigate how to best represent a parabolic graph using a function description.

All parabolas are denoted as either a " U " or inverted " U ". There are two principal parameters of a parabola. The vertex i.e the maximum or minimum point attained by the parabola. The line of symmetry or focus point: The line of symmetry can either be vertical or horizontal but it always passes through the focus point.

We are given a graph of a parabola that has two zeros which can be read off from the plot.

We will locate these zeros and write them down:

`\begin{gathered} x\text{ = 3} \\ x\text{ = 5} \end{gathered}`

All parabolas are expressed by a quadratic polynomial function. The quadratic polynomial can be expressed in factorized form as follows:

`(\text{ x - }\alpha\text{ )}\cdot(x\text{ - }\beta\text{ )}`

Where,

`\begin{gathered} \alpha\text{ = 3 ( First Zero )} \\ \beta\text{ = 5 , ( Second Zero )} \end{gathered}`

We will express our located zeros in the factorized quadratic expressed above:

`(\text{ x - 3 )}\cdot(x\text{ - 5 )}`

Then we will try to solve the parenthesis and expand the factorized form as follows:

`\begin{gathered} -5\cdot(x\text{ - 3 ) + x}\cdot(x\text{ - 3 )} \\ -5x+15+x^2\text{ - 3x} \end{gathered}`

Group the similar terms and simplify:

`x^2\text{ - 8x + 15 }`

Therefore the function that best describes the given plot is:

`y=x^2\text{ -8x + 15 }\ldots\text{ Option A}`