Final answer:
The quadratic equation in factored form using the x-intercepts (2,0) and (4,0), and the point (5,-3) is y = -1(x - 2)(x - 4).
Step-by-step explanation:
To write the equation in factored form using the x-intercepts (2,0) and (4,0), and the point (5,-3), we start by setting up the factored form of the quadratic equation, based on the x-intercepts:
y = a(x - 2)(x - 4)
Next, we need to find the value of 'a' using the given point (5, -3). Substituting x = 5 and y = -3 into the equation gives us:
-3 = a(5 - 2)(5 - 4)
-3 = 3a
Divide both sides by 3 to find 'a':
a = -1
Now that we have 'a', we can write the full equation in factored form:
y = -1(x - 2)(x - 4)
Or, after expanding:
y = -(x^2 - 6x + 8)
This is the factored form of the quadratic equation using the given x-intercepts and the point.