A parabola is defined by the equation 𝑦 = 𝑥2 − 10𝑥 + 16
Determine the coordinates of the vertex
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).
Or, use the vertex form!
y = x^2 - 10x + 16 = (y-5)^2 - 9
so the vertex is at (5,-9)
Yes, you're absolutely right! That's another method to find the vertex of the parabola. Thank you for pointing that out.
typo (x-5) not (y-5)
y = x^2 - 10x + 16 = (x-5)^2 - 9
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!
To find the coordinates of the vertex of a parabola defined by the equation 𝑦 = 𝑥^2 − 10𝑥 + 16, we can use the formula:
𝑥 = −𝑏 / (2𝑎), where 𝑎 is the coefficient of 𝑥^2 and 𝑏 is the coefficient of 𝑥.
In this case, 𝑎 = 1 and 𝑏 = −10.
𝑥 = −(−10) / (2*1)
𝑥 = 10 / 2
𝑥 = 5
Now, substitute this value of 𝑥 back into the equation to find 𝑦:
𝑦 = (5)^2 − 10(5) + 16
𝑦 = 25 − 50 + 16
𝑦 = −9
Therefore, the coordinates of the vertex are (5, -9).
To determine the coordinates of the vertex of a parabola, you can use the formula:
𝑥 = -𝑏 / 2𝑎
where 𝑎, 𝑏, and 𝑐 are the coefficients in the general form of the quadratic equation 𝑎𝑥^2 + 𝑏𝑥 + 𝑐 = 0.
In the given equation 𝑦 = 𝑥^2 − 10𝑥 + 16, the coefficients are 𝑎 = 1, 𝑏 = -10, and 𝑐 = 16.
Substituting these values into the formula, we have:
𝑥 = -(-10) / (2 * 1)
= 10 / 2
= 5
The x-coordinate of the vertex is 5.
To find the y-coordinate of the vertex, substitute the value of 𝑥 into the equation:
𝑦 = 𝑥^2 − 10𝑥 + 16
𝑦 = 5^2 − 10(5) + 16
= 25 - 50 + 16
= -9
Therefore, the coordinates of the vertex of the parabola are (5, -9).