A parabola is defined by the equation 𝑦 = 𝑥2 − 10𝑥 + 16. Determine the coordinates of the vertex

Answer 1

of the parabola.

To find the vertex of the parabola given in this equation, we can first rearrange the equation into vertex form:

𝑦 = 𝑥^2 − 10𝑥 + 16
= (𝑥^2 − 10𝑥 + 25) − 9
= (𝑥 − 5)^2 − 9

The vertex form of a parabola is (h, k), where h is the x-coordinate of the vertex and k is the y-coordinate of the vertex.

In this equation, we can see that the x-coordinate of the vertex is 5 (since the 𝑥 − 5 term is squared and thus always positive). To find the y-coordinate of the vertex, we can simply evaluate the equation when 𝑥 = 5:

𝑦 = (5 − 5)^2 − 9 = -9

Therefore, the vertex of the parabola is at (5, -9).