A parabola is defined by the equation 𝑦 = 𝑥2 − 10𝑥 + 16 b)
Identify the 𝑥-intercepts of the parabola
To find the 𝑥-intercepts of the parabola, we set y = 0 and solve for x:
0 = x^2 - 10x + 16
We can factor the quadratic as (x-2)(x-8) = 0, or use the quadratic formula:
x = [10 ± √(10^2 - 4(1)(16))] / 2
x = [10 ± √36] / 2
x = 5 ± 3
So the 𝑥-intercepts of the parabola are at x = 2 and x = 8.
To find the x-intercepts of a parabola, we need to set y = 0 in the equation and solve for x.
Given equation: 𝑦 = 𝑥^2 − 10𝑥 + 16
Setting y = 0:
0 = 𝑥^2 − 10𝑥 + 16
To solve this quadratic equation, we can either factor it or use the quadratic formula.
Factoring:
0 = (𝑥 − 2)(𝑥 − 8)
Setting each factor equal to zero:
𝑥 − 2 = 0 -> 𝑥 = 2
𝑥 − 8 = 0 -> 𝑥 = 8
Therefore, the x-intercepts of the parabola are x = 2 and x = 8.