A parabola is defined by the equation 𝑦 = 𝑥2 − 10𝑥 + 16
Identify the 𝑥-intercepts of the parabola.
To find the 𝑥-intercepts of a parabola, we set 𝑦 equal to zero and solve for 𝑥.
So, the equation becomes:
0 = 𝑥2 − 10𝑥 + 16
We can factor this equation as:
0 = (𝑥 − 2)(𝑥 − 8)
To find the 𝑥-intercepts, we set each factor equal to zero:
𝑥 − 2 = 0 or 𝑥 − 8 = 0
Solving for 𝑥, we get:
𝑥 = 2 or 𝑥 = 8
Therefore, the 𝑥-intercepts of the parabola are (2, 0) and (8, 0).
To identify the x-intercepts of a parabola, we need to find the values of x when y is equal to zero. We can set the equation for the parabola equal to zero:
𝑦 = 𝑥^2 − 10𝑥 + 16
0 = 𝑥^2 − 10𝑥 + 16
Next, we can solve this quadratic equation by factoring or by using the quadratic formula. We will use factoring in this case.
Since the coefficient of 𝑥^2 is 1, we can easily factor the quadratic equation as follows:
0 = (𝑥−4)(𝑥−4)
Setting each factor equal to zero, we get:
𝑥−4 = 0
𝑥 = 4
Therefore, the x-intercept of the parabola is 𝑥 = 4.