A quadratic function has x-intercepts 2 and 6 and its vertex is (4, 8). What is the corresponding quadratic expression?
Obviously y = a(x-2)(x-6)
Since y(4) = 8, a = -2 and
y = -2(x-2)(x-6)
= -2((x-4)^2 - 4)
= -2x^2 + 16x - 24
To find the quadratic expression, we need to know that the x-intercepts of the quadratic function are the values of x where the function intersects the x-axis.
If the x-intercepts are 2 and 6, it means that when x = 2 and x = 6, the quadratic function evaluates to 0.
We can express this information using the factored form of a quadratic equation:
(x - 2)(x - 6) = 0
Now, let's expand this equation:
x^2 - 2x - 6x + 12 = 0
Combining like terms:
x^2 - 8x + 12 = 0
So, the corresponding quadratic expression is:
f(x) = x^2 - 8x + 12