Question

The equation f(x) = 5x2 − 30x + 6 represents a parabola. What is the vertex of the parabola?

(−5, 281)
(5, −19)
(−3, 141)
(3, −39)

Answer 1

The answer is D. (3,-39)

Just plug the numbers into the formula to find the Parabola.

f(x) = ax
`x^(2)`+ bx + c

Then find X:

x = -
`(b)/(2a)`
Then solve.

Hope this helped. Have a great day!

Answer 2

D.
`(3,-39)`

Explanation:

We have been given an equation
`f(x)=5x^2-30x+6`. We are asked to find the vertex of parabola for our given equation.

We will use formula
`x=(-b)/(2a)` to find the x-coordinate of the vertex of parabola, then we will substitute the value of x-coordinate in our equation to find the y-coordinate of the parabola.

`x=(-(-30))/(2*5)`

`x=(30)/(10)`

`x=3`

Therefore, the x-coordinate of the vertex of the parabola is 3.

Now let us substitute
`x=3` in our given equation to find the y-coordinate of the parabola.

`f(3)=5(3)^2-30(3)+6`

`f(3)=5*9-90+6`

`f(3)=45-90+6`

`f(3)=51-90`

`f(3)=-39`

So, the y-coordinate of the vertex of parabola is
`-39`. The point
`(3,-39)` represents the vertex of the parabola represented by our given equation and option D is the correct choice.