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