A parabola is defined by the equation 𝑦 = 𝑥2 − 10𝑥 + 16
find Identify the 𝑥-intercepts of the parabola
To find the 𝑥-intercepts of the parabola, we need to set 𝑦 equal to zero:
0 = 𝑥2 − 10𝑥 + 16
We can factor the quadratic equation as:
0 = (𝑥 − 2)(𝑥 − 8)
Therefore, the 𝑥-intercepts of the parabola are 2 and 8.
To find the x-intercepts of a parabola, we need to find the values of x when y equals zero.
We can set y = 0 in the equation y = x^2 - 10x + 16 and solve for x.
0 = x^2 - 10x + 16
To solve this quadratic equation, we can factorize, complete the square, or use the quadratic formula.
Let's factorize the equation:
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.