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)
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 = - \(\frac{b}{2a}\)
Then solve.
Hope this helped. Have a great day!
Answer:
D. \((3,-39)\)
Step-by-step 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 \(x=\frac{-b}{2a}\) 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.
\(x=\frac{-(-30)}{2*5}\)
\(x=\frac{30}{10}\)
\(x=3\)
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.