5. A parabola is defined by the equation 𝑦 = 𝑥2 − 10𝑥 + 16.
c) State the equation of the axis of symmetry.
The axis of symmetry is a vertical line that passes through the vertex of the parabola. Its equation is given by:
𝑥 = −𝑏/2𝑎
where 𝑏 is the coefficient of the linear term (−10) and 𝑎 is the coefficient of the quadratic term (1) in the equation 𝑦 = 𝑎𝑥2 + 𝑏𝑥 + 𝑐.
Substituting these values, we get:
𝑥 = −(−10)/2(1)
𝑥 = 5
Therefore, the equation of the axis of symmetry is 𝑥 = 5.
To find the equation of the axis of symmetry of a parabola, you can use the formula:
𝑥 = -𝑏 / (2𝑎)
In the given equation 𝑦 = 𝑥2 − 10𝑥 + 16, a is the coefficient of 𝑥^2, which is 1, and b is the coefficient of 𝑥, which is -10.
Substituting these values into the formula, we get:
𝑥 = -(-10) / (2 * 1)
𝑥 = 10 / 2
𝑥 = 5
Therefore, the equation of the axis of symmetry is 𝑥 = 5.