A parabola is defined by the equation 𝑦 = 𝑥2 − 10𝑥 + 16.
a) Write the equation in factored form
To write the equation in factored form, we need to first factor out the coefficient of the squared term, which is 1:
y = x^2 - 10x + 16
Next, we need to find two numbers that multiply to 16 and add up to -10 (the coefficient of the x term). These numbers are -2 and -8:
y = (x - 2)(x - 8)
Therefore, the equation in factored form is y = (x - 2)(x - 8).
To write the equation of the parabola in factored form, we need to determine the factors of the quadratic equation 𝑦 = 𝑥^2 − 10𝑥 + 16 and rewrite it in the form 𝑦 = (𝑥 − 𝑎)(𝑥 − 𝑏), where 𝑎 and 𝑏 are the values of the factors.
First, let's find the factors of the quadratic equation.
The constant term, 16, can be factored as 1 × 16 or 2 × 8.
Now, let's determine which of these factor pairs will add up to give the coefficient of the linear term, -10.
By trying out the pairs, we find that -2 and -8 add up to -10.
Therefore, we can express the equation in factored form as 𝑦 = (𝑥 − 2)(𝑥 − 8).