Use your calculator or other handheld technology to graph \( y=4 x^{2}-24 x+38 \). Then answer the following questions. What is the vertex of the graph? Give your answer in coordinate form. The vertex is

To find the vertex of the quadratic equation \( y = 4x^2 - 24x + 38 \), you can use the vertex formula, which is \( x = -\frac{b}{2a} \). Here, \( a = 4 \) and \( b = -24 \). Plugging in the values gives \( x = -\frac{-24}{2 \cdot 4} = 3 \). To find the y-coordinate, substitute \( x = 3 \) back into the equation, yielding \( y = 4(3^2) - 24(3) + 38 = 38 - 72 + 38 = 4 \). Thus, the vertex is (3, 4). Now, if you were to visualize this quadratic function on your graphing calculator, you'd see a lovely upward opening parabola with its tip (vertex) at the genial point (3, 4). Doesn’t it feel satisfying to pinpoint that sweet spot where the quadratic takes a break before rising up again?