Given the quadratic function f(x) = 16x^2 – 64x + 64, find a value of x such that f(x) = 16.
16 = 16x^2 - 64x + 64
0 = 16x^2 - 64x + 64 - 16
(using quadratic formula)
x= 3 or x =1
To find a value of x such that f(x) = 16, we need to solve the quadratic equation 16x^2 – 64x + 64 = 16.
Step 1: Start by subtracting 16 from both sides of the equation, which gives us 16x^2 – 64x + 48 = 0.
Step 2: Divide the entire equation by 16 to simplify it, resulting in x^2 – 4x + 3 = 0.
Step 3: Now we need to factorize the quadratic equation. We look for two numbers whose product is 3 and whose sum is -4. The numbers are -1 and -3, so we can rewrite the equation as (x - 1)(x - 3) = 0.
Step 4: Set each factor equal to zero and solve for x.
x - 1 = 0 ----> x = 1
x - 3 = 0 ----> x = 3
So, the values of x that satisfy the equation f(x) = 16 are x = 1 and x = 3.