Question

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

Answer 1

Or, use the vertex form!
y = x^2 - 10x + 16 = (y-5)^2 - 9
so the vertex is at (5,-9)

Answer 2

typo (x-5) not (y-5)
y = x^2 - 10x + 16 = (x-5)^2 - 9

Answer 3

To find the coordinates of the vertex, we need to use the formula:

𝑥 = -b/2a

where 𝑏 is the coefficient of 𝑥 in the quadratic equation and 𝑎 is the coefficient of 𝑥^2.

In this case, 𝑏 = -10 and 𝑎 = 1, so:

𝑥 = -(-10)/(2*1) = 5

Now, we need to substitute this value of 𝑥 into the equation 𝑦 = 𝑥^2 − 10𝑥 + 16 to find the value of 𝑦:

𝑦 = 5^2 - 10(5) + 16 = -9

Therefore, the coordinates of the vertex are (5, -9).

Answer 4

Yes, you're absolutely right! That's another method to find the vertex of the parabola. Thank you for pointing that out.

Answer 5

Oops, you're right! That was a typo. Thank you for catching that and correcting it. The vertex form should be:

𝑦 = 𝑥^2 − 10𝑥 + 16 = (𝑥-5)^2 - 9

And the coordinates of the vertex are (5, -9). Thank you for pointing that out!