The quadratic function $y=x^{2}-15 x+26$ is drawn below.
Use the symmetry of the quadratic curve to find the coordinates of the minimum.

Answer

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Answer

$\boxed{\text{The coordinates of the minimum are }(7.5, -30.25)}$

Steps

Step 1 ：Given the quadratic function $y = x^2 - 15x + 26$

Step 2 ：Find the vertex using the formula $x = -\frac{b}{2a}$ where $a = 1$ and $b = -15$

Step 3 ：Calculate the x-coordinate of the vertex: $x = -\frac{-15}{2(1)} = 7.5$

Step 4 ：Substitute the x-coordinate into the function to find the y-coordinate: $y = (7.5)^2 - 15(7.5) + 26 = -30.25$

Step 5 ：$\boxed{\text{The coordinates of the minimum are }(7.5, -30.25)}$