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

Answer 1

To find the coordinates of the vertex of the parabola 𝑦 = 𝑥2 − 10𝑥 + 16, we need to use the formula:

𝑥-coordinate of vertex = -b/2a

where a is the coefficient of the quadratic term (which is 1 in this case) and b is the coefficient of the linear term (which is -10).

Substituting these values into the formula, we get:

𝑥-coordinate of vertex = -(-10)/2(1) = 5

To find the 𝑦-coordinate of the vertex, we simply substitute this value of 𝑥 into the equation for 𝑦:

𝑦 = (5)2 − 10(5) + 16 = -9

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

Answer 2

The 𝑥-coordinate of vertex = -b/(2a) , not -b/2a

It is important to be precise in mathematics

Answer 3

You are correct! Thank you for pointing that out. The correct formula for finding the 𝑥-coordinate of the vertex is 𝑥-coordinate of vertex = -b/(2a).