A parabola is defined by the equation 𝑦 = 𝑥2 − 10𝑥 + 16
d) Determine the coordinates of the vertex.
To find the coordinates of the vertex of the parabola, we need to use the formula:
𝑥 = -𝑏/2𝑎
where 𝑎 and 𝑏 are the coefficients of the quadratic equation 𝑦 = 𝑎𝑥2 + 𝑏𝑥 + 𝑐.
In this case, 𝑎 = 1 and 𝑏 = -10. Substituting these values into the formula, we get:
𝑥 = -(-10)/2(1) = 5
Now we can find the value of 𝑦 at this point by substituting 𝑥 = 5 into the equation:
𝑦 = (5)2 - 10(5) + 16 = -9
Therefore, the vertex of the parabola is at the point (5, -9).
To find the coordinates of the vertex of a parabola given by the equation 𝑦 = 𝑥^2 − 10𝑥 + 16, we can use the formula 𝑥 = −𝑏 / (2𝑎) to find the x-coordinate of the vertex.
Comparing the equation to the standard form 𝑦 = 𝑎𝑥^2 + 𝑏𝑥 + 𝑐, we can see that a = 1, b = -10, and c = 16.
𝑥 = −𝑏 / (2𝑎)
𝑥 = −(−10) / (2(1))
𝑥 = 10 / 2
𝑥 = 5
Now that we have the x-coordinate of the vertex, we can substitute it back into the equation 𝑦 = 𝑥^2 − 10𝑥 + 16 to find the y-coordinate.
𝑦 = (5)^2 − 10(5) + 16
𝑦 = 25 − 50 + 16
𝑦 = -9
Therefore, the coordinates of the vertex are (5, -9).