\( y=\frac{2}{3} x^{2}-8 x+7 \) 17. Will the parabola open up or down? open up 18. Is the vertex a minimum or maximum? Min. 19. Find the vertex. 20. Find the Axis of Symmetry.

The parabola will open up because the coefficient of \( x^{2} \) in the equation \( y = \frac{2}{3} x^{2} - 8x + 7 \) is positive. This means that as you move away from the vertex in both directions, the value of \( y \) will increase. The vertex can be found using the formula \( x = -\frac{b}{2a} \). Here, \( a = \frac{2}{3} \) and \( b = -8 \). Plugging in the values, \( x = -\frac{-8}{2 \cdot \frac{2}{3}} = 6 \). To find the corresponding \( y \)-value, substitute \( x = 6 \) back into the equation: \( y = \frac{2}{3}(6^{2}) - 8(6) + 7 = -1 \). Therefore, the vertex is at (6, -1). The axis of symmetry for a parabola given by the standard form \( y = ax^{2} + bx + c \) is the vertical line that passes through the vertex. Since we found that the vertex occurs at \( x = 6 \), the axis of symmetry is the line \( x = 6 \). This means if you were to fold the parabola along this line, both halves would match perfectly, just like a well-folded piece of paper!