Identify the 𝑥-intercepts of the parabola. A parabola is defined by the equation 𝑦 = 𝑥2 − 10𝑥 + 16.
To find the 𝑥-intercepts of a parabola, we set 𝑦 = 0 in the equation and solve for 𝑥.
0 = 𝑥2 − 10𝑥 + 16
We can factor this trinomial:
0 = (𝑥 − 2)(𝑥 − 8)
Using the zero product property, we know that either 𝑥 − 2 = 0 or 𝑥 − 8 = 0.
So the 𝑥-intercepts are 𝑥 = 2 and 𝑥 = 8.
To find the 𝑥-intercepts of the parabola defined by the equation 𝑦 = 𝑥^2 − 10𝑥 + 16, we need to find the values of 𝑥 when 𝑦 is equal to zero.
Setting 𝑦 = 0, the equation becomes:
0 = 𝑥^2 − 10𝑥 + 16
To solve this equation, we can factor or use the quadratic formula. Let's use the quadratic formula:
𝑥 = (−𝑏 ± √(𝑏^2 − 4𝑎𝑐)) / (2𝑎)
In our case, 𝑎 = 1, 𝑏 = −10, and 𝑐 = 16. Substituting these values into the formula, we get:
𝑥 = (−(−10) ± √((−10)^2 − 4(1)(16))) / (2(1))
𝑥 = (10 ± √(100 − 64)) / 2
𝑥 = (10 ± √36) / 2
𝑥 = (10 ± 6) / 2
Simplifying further, we have two possibilities:
1. 𝑥 = (10 + 6) / 2
𝑥 = 16 / 2
𝑥 = 8
2. 𝑥 = (10 - 6) / 2
𝑥 = 4 / 2
𝑥 = 2
Therefore, the 𝑥-intercepts of the parabola are 𝑥 = 8 and 𝑥 = 2.