ANSWER
Vertex: (3/2, -3)
Axis of symmetry: x = 3/2
x-intercept: 0 and 3
Maximum or minimum: Minimum
Max/Min value: -3
y-intercept: 0
EXPLANATION
We have the quadratic function given in the question.
The vertex of a quadratic function (parabola) is the point where the parabola is either at its minimum or its maximum.
The parabola given has a minimum.
A quadratic function is generally given as:
[tex]f(x)=ax^2\text{ + bx + c}[/tex]where a, b and c are coefficients
The x coordinate of the vertex is gotten by using:
x = - b / 2a
and the y coordinate is gotten by putting the x value in the function.
So, we have:
[tex]\begin{gathered} x\text{ = -}\frac{-4}{2(\frac{4}{3})}\text{ = -}\frac{-4}{\frac{8}{3}}\text{ = -(-4 }\cdot\text{ }\frac{3}{8}) \\ x=\text{ }\frac{3}{2} \end{gathered}[/tex]This implies that:
[tex]\begin{gathered} g(x)\text{ = }\frac{4}{3}(\frac{3}{2})^2-\text{ 4(}\frac{3}{2}) \\ g(x)\text{ = 3 - 6} \\ g(x)\text{ = -3} \end{gathered}[/tex]The vertex is (3/2, -3)
The axis of symmetry is given as the x coordinate of the vertex. That is:
x = 3/2
The x intercepts are the points where the function crosses the x axis (horizontal axis).
The x intercepts are 0 and 3.
The function has been determined to have a minimum value. The minimum value is the lowest value of the function. It is the y coordinate of the vertex.
Therefore, the minimum value is -3.
The y intercept is the point where the function crosses the y axis (vertical axis).
The y intercept is 0.