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

$The coordinates of the minimum are (7.5, - 30.25)$

Steps

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

Step 2 ：Find the vertex using the formula $x = - \frac{b}{2 a}$ 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 ： $The coordinates of the minimum are (7.5, - 30.25)$