Answer:
Vertex: [tex](-\frac{1}{3},-\frac{25}{3})[/tex]
Y-intercept: [tex](0,-8)[/tex]
Step-by-step explanation:
The x-coordinate of the vertex would be [tex]x=\frac{-b}{2a}[/tex] and the y-coordinate of the vertex is whatever the output is given the value of x.
Therefore, the x-coordinate of the vertex is [tex]x=\frac{-b}{2a}=\frac{-2}{2(3)}=\frac{-2}{6}=-\frac{1}{3}[/tex]
This means the y-coordinate of the vertex is [tex]y=3x^2+2x-8=3(-\frac{1}{3})^2+2(-\frac{1}{3})-8=3(\frac{1}{9})-\frac{2}{3}-8=\frac{1}{3}-\frac{2}{3}-8=-\frac{1}{3}-8=-\frac{1}{3}-\frac{24}{3}=-\frac{25}{3}[/tex]
So, the vertex is [tex](-\frac{1}{3},-\frac{25}{3})[/tex]
The y-intercept of a function is the y-value at which x=0, or the y-value when the function crosses the y-axis. Therefore, if we plug x=0 into the function, we see that [tex]h(0)=3(0)^2+2(0)-8=0+0-8=-8[/tex], so our y-intercept is -8 or (0,-8).
I attached a graph below to help you visualize the vertex and y-intercept given the function.
