. A parabola is defined by the equation 𝑦 = 𝑥2 − 10𝑥 + 16.State the equation of the axis of symmetry
The equation of the axis of symmetry for a parabola of the form 𝑦 = 𝑎𝑥2 + 𝑏𝑥 + 𝑐 is given by 𝑥 = -𝑏/2𝑎.
In this case, 𝑦 = 𝑥2 − 10𝑥 + 16, so 𝑎 = 1, 𝑏 = -10, and 𝑐 = 16.
Therefore, the equation of the axis of symmetry is:
𝑥 = -𝑏/2𝑎 = -(-10)/2(1) = 5
So the equation of the axis of symmetry is 𝑥 = 5.
To find the equation of the axis of symmetry for a parabola defined by the equation 𝑦 = 𝑥^2 − 10𝑥 + 16, we can use the formula 𝑥 = −𝑏/2𝑎, where 𝑎 and 𝑏 are the coefficients of the quadratic equation.
In this case, 𝑎 = 1 and 𝑏 = -10. Therefore, we substitute these values into the formula:
𝑥 = -(-10)/2(1)
= 10/2
= 5
Hence, the equation of the axis of symmetry is 𝑥 = 5.