A parabola is defined by the equation 𝑦 = 𝑥2 − 10𝑥 + 16.Determine the coordinates of the vertex
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).
The 𝑥-coordinate of vertex = -b/(2a) , not -b/2a
It is important to be precise in mathematics
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).
To find the coordinates of the vertex of a parabola defined by the equation 𝑦 = 𝑥^2 − 10𝑥 + 16, we can use the formula for the x-coordinate of the vertex: 𝑥 = -𝑏 / 2𝑎.
In this equation, 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).
Let's substitute these values into the formula:
𝑥 = -(-10) / 2(1)
𝑥 = 10 / 2
𝑥 = 5
Now, to find the y-coordinate of the vertex, we substitute the value of 𝑥 back into the original equation:
𝑦 = (5)^2 - 10(5) + 16
𝑦 = 25 - 50 + 16
𝑦 = -9
Therefore, the coordinates of the vertex are (5, -9).