A parabola is defined by the equation 𝑦 = 𝑥2 − 10𝑥 + 16.
Identify the 𝑥-intercepts of the parabola.
To find the x-intercepts, we set y equal to zero:
0 = 𝑥2 − 10𝑥 + 16
We can factor the quadratic equation:
0 = (𝑥 − 2)(𝑥 − 8)
Using the zero product property, we know that either (𝑥 − 2) or (𝑥 − 8) must be equal to zero. So the x-intercepts are:
𝑥 = 2 and 𝑥 = 8.
To identify the x-intercepts of the parabola, we need to find the values of x when y = 0.
Setting y = 0, we have the equation 0 = x^2 - 10x + 16.
To solve this equation, we can either factor it or use the quadratic formula.
Factoring:
To factor the equation, we need to find two numbers that multiply to give us 16 and add up to -10. These numbers are -2 and -8.
Thus, we can rewrite the equation as:
0 = (x - 2)(x - 8).
Setting each factor equal to zero, we have:
x - 2 = 0, which gives x = 2.
and
x - 8 = 0, which gives x = 8.
Therefore, the x-intercepts of the parabola are x = 2 and x = 8.