Given the quadratic function f(x) = 16x2 – 64x + 64, find a value of x such that f(x) = 16.
f(x) = 16x2 – 64x + 64
for f(x)=16, write:
16=16x² - 64x +64
transpose 16 to the right, and factor out numeric factor 16:
16(x² -4x +3) = 0
Factor expression
16(x-3)(x-1)=0
This means that x=3 or x=1, either one of which satisfies the equation
f(x)=16.
Check by substituting x=3 or x=1 in f(x).
To find a value of x such that f(x) = 16 for the given quadratic function f(x) = 16x^2 – 64x + 64, we need to solve the equation f(x) = 16.
1. Start with the quadratic function f(x) = 16x^2 – 64x + 64.
2. Replace f(x) with 16: 16 = 16x^2 – 64x + 64.
3. Subtract 16 from both sides to set the equation equal to zero: 16x^2 – 64x + 48 = 0.
4. Divide the entire equation by 16 to simplify: x^2 – 4x + 3 = 0.
Now, we can solve this equation by factoring or using the quadratic formula. Let's use factoring:
5. Factor the quadratic expression x^2 – 4x + 3 = 0: (x – 3)(x – 1) = 0.
6. Set each factor equal to zero and solve for x:
- x – 3 = 0 ---> x = 3
- x – 1 = 0 ---> x = 1
So, the values of x that satisfy f(x) = 16 for the given quadratic function are x = 3 and x = 1.