Answer:
[tex](4,-40)[/tex]
Step-by-step explanation:
We have been given an equation [tex]f(x)=3x^2-24x+8[/tex] that represents a parabola. We are asked to find the vertex of parabola.
We will use vertex formula: [tex]\frac{-b}{2a}[/tex] to find the x-coordinate of vertex of parabola.
[tex]\frac{-(-24)}{2*3}[/tex]
[tex]\frac{24}{6}[/tex]
[tex]4[/tex]
So the x-coordinate of vertex of parabola is 4. Now we will substitute [tex]x=4[/tex] in our given equation to find the y-coordinate of vertex.
[tex]f(4)=3*4^2-24*4+8[/tex]
[tex]f(4)=3*16-96+8[/tex]
[tex]f(4)=48-96+8[/tex]
[tex]f(4)=56-96[/tex]
[tex]f(4)=-40[/tex]
Since the y-coordinate of vertex of parabola is -40, therefore, the vertex of our given parabola is at point [tex](4,-40)[/tex].
